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arxiv: 2606.28945 · v1 · pith:MNDHHH3Znew · submitted 2026-06-27 · 🧮 math-ph · math.CO· math.MP· math.PR· math.RT

The heat-kernel master field on mathbb{Z}^d at strong coupling

Thibaut Lemoine This is my paper

Pith reviewed 2026-06-30 08:16 UTC · model grok-4.3

classification 🧮 math-ph math.COmath.MPmath.PRmath.RT
keywords large-N Yang-Millsheat-kernel actionmaster fieldWilson loopsstrong couplinglattice gauge theory1/N expansionarea law
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The pith

Normalized Wilson loop expectations in large-N Yang-Mills on Z^d at strong coupling have infinite-volume limits that factorize at leading 1/N order and admit an all-order expansion with exponentially local coefficients.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proves that for the heat-kernel action on the d-dimensional integer lattice with d at least 2, the normalized expectations of Wilson loops converge in the infinite-volume limit as N goes to infinity. These limits factorize at the leading order in 1/N and possess a complete asymptotic expansion in powers of 1/N whose coefficients decay exponentially away from the loop. The leading term of the expansion defines the master field, which satisfies an area-law upper bound. The argument relies on a rooted master loop equation that incorporates plaquette decorations and on a strong-coupling trajectory expansion that isolates the leading contribution.

Core claim

Normalized Wilson loop expectations have infinite-volume large-N limits, factorize at leading order, and admit an all-order 1/N-expansion with exponentially local coefficients, whose leading order characterizes the master field. An area-law upper bound holds for the heat-kernel master field, with a stronger coefficientwise version.

What carries the argument

The rooted heat-kernel master loop equation on the extended space of loop observables coupled to compactly supported plaquette decorations, together with the strong-coupling order-truncated rooted trajectory expansion that identifies the leading term.

If this is right

  • Wilson loop expectations converge in the infinite-volume limit at large N.
  • The leading large-N term factorizes and is given by the master field.
  • The full 1/N expansion exists with coefficients that are exponentially local in the lattice distance.
  • The master field obeys an area-law upper bound, including a coefficientwise strengthening.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same master-field characterization may apply to other lattice actions whose loop equations admit similar rooted expansions at strong coupling.
  • The exponentially local coefficients suggest that the master field can be approximated by finite-cluster computations on the lattice.
  • The area-law bound on the master field supplies an upper bound on the string tension that is uniform in the coupling regime considered.

Load-bearing premise

The rooted heat-kernel master loop equation closes on the extended space of loop observables coupled to compactly supported plaquette decorations.

What would settle it

A direct computation of finite-N Wilson loop expectations at strong coupling whose large-N limit fails to factorize or whose 1/N coefficients fail to be exponentially local would falsify the central claim.

Figures

Figures reproduced from arXiv: 2606.28945 by Thibaut Lemoine.

Figure 1
Figure 1. Figure 1: Orientation convention of sublattices of Z 2 and Z 3 . A finite lattice Λ ⊂ Z d is a finite connected two-dimensional subcomplex of this cubical complex. We denote by E(Λ) and P(Λ) its unoriented edges and plaquettes. Once and for all we choose one orientation of every unoriented edge and plaquette, and we denote the resulting oriented sets by E(Λ) and P(Λ), see [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: An example of stable highest weight [λ +, λ−]N with only one zero. In stable coordinates, the Casimir becomes easier to analyze in the large-N regime: for each cell □ in the Young diagram associated to λ + or λ −, if we write (i, j) its coordinates in the diagram, the content of the cell is defined by c(□) = c(i, j) = j − i. The total content is a map K : P → Z that assigns to a partition the sum of conten… view at source ↗
Figure 3
Figure 3. Figure 3: An example of walled-Brauer diagram τ ∈ B4,3. The following result will be important later; it is the standard walled-Brauer expansion of the mixed Schur–Weyl projector, in the form used for instance in [Dah26, Lem26] [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: A portion of the Young graph (left), and the corresponding portion of the 2-truncated Young graph (right). We shall use the standard Cartesian product of graphs. If G and H are two unoriented graphs, their Cartesian product G□H is the graph with vertex set V (G□H) = V (G) × V (H), 4There is a boundary case when N = ℓ(α) + ℓ(β), but it is irrelevant in the stable range considered below [PITH_FULL_IMAGE:fig… view at source ↗
Figure 5
Figure 5. Figure 5: The dual incidence graph of a lattice Λ ⊂ Z 2 with a Wilson loop insertion. The construction proceeds locally: a plaquette character χαp (U∂p) is resolved into tensor legs distributed along the boundary incidences (p, e), then each non-tree edge variable Ue is integrated independently. The integral at e is the orthogonal projection onto the invariant subspace of the tensor product of all representation spa… view at source ↗
Figure 6
Figure 6. Figure 6: Two local channel examples: one with no Wilson loop insertion (left) and one with a Wilson loop insertion (right) [PITH_FULL_IMAGE:figures/full_fig_p020_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: A local channel representation of the dual incidence graph illustrated in [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: A dual incidence graph illustrating the peeling process. The connected active support Ylow (in light blue) will be peeled in the displayed order: p34 → p44 → p43. The remaining residual core is Core∗(Ylow) = {p31, p32, p33}. edge vertices in this support are vacuum vertices; we denote them by f1 = (p33, p43), f2 = (p43, p44), f3 = (p44, p34). With this notation the active incidence graph of Ylow is the cha… view at source ↗
Figure 9
Figure 9. Figure 9: Local representations of splittings and mergers. The dotted parts may be arbitrary lattice paths. Define σcj(x, y) = ( −1, x and y have the same sign, +1, x and y have opposite signs [PITH_FULL_IMAGE:figures/full_fig_p040_9.png] view at source ↗
read the original abstract

We solve large-$N$ Yang--Mills theory on $\mathbb{Z}^d$, for every $d\geq2$, at strong coupling, for structure group $\mathrm{U}(N)$ and for the heat-kernel action. More precisely, we prove that normalized Wilson loop expectations have infinite-volume large-$N$ limits, factorize at leading order, and admit an all-order $1/N$-expansion with exponentially local coefficients, whose leading order characterizes the master field. We also prove an area-law upper bound for the heat-kernel master field, with a stronger coefficientwise version. The proof is based on a rooted heat-kernel master loop equation. Unlike the Wilson-action equation or the two-dimensional Makeenko--Migdal equation, this equation does not close on Wilson loop observables alone; it closes on an extended space of loop observables coupled to compactly supported plaquette decorations. We prove a strong-coupling, order-truncated rooted trajectory expansion and then identify its leading term with the master field. The main inputs are the universal finite-$N$ duality formulas developed in the companion paper \cite{Lem26a} and large-$N$ heat-kernel estimates from \cite{LemMai25,LM2}.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The paper proves that normalized Wilson loop expectations in U(N) Yang-Mills theory on the lattice Z^d (d≥2) with the heat-kernel action at strong coupling admit infinite-volume large-N limits. These limits factorize at leading order, possess an all-order 1/N-expansion whose coefficients are exponentially local, and the leading term defines the master field. A coefficientwise area-law upper bound is also established for the heat-kernel master field. The argument proceeds from a rooted heat-kernel master loop equation that closes on an extended space of decorated loop observables, followed by a strong-coupling order-truncated rooted trajectory expansion whose leading term is identified with the master field; the derivation invokes universal finite-N duality formulas from a companion paper together with large-N heat-kernel estimates from prior works.

Significance. If the claims hold, the work supplies a rigorous construction of the master field for the heat-kernel action in all dimensions d≥2 at strong coupling, together with explicit control on the 1/N expansion and an area-law bound. The use of the extended decorated-loop space and the rooted trajectory expansion provides a concrete mechanism for closing the loop equations that differs from the Wilson-action or two-dimensional Makeenko-Migdal settings. The results are parameter-free once the strong-coupling regime is fixed and rest on explicit expansions rather than abstract existence arguments.

minor comments (3)
  1. [§1] §1 (Introduction): the statement that the rooted equation 'closes on an extended space' would benefit from a one-sentence pointer to the precise definition of the decoration space (e.g., the support condition on plaquette insertions) before the trajectory expansion is introduced.
  2. [§2] The dependence on the duality formulas of Lem26a and the estimates of LemMai25/LM2 is stated clearly in the abstract and §2, but a short table or paragraph listing the exact theorem numbers invoked at each step of the truncation argument would improve readability for readers who have not yet consulted the companion papers.
  3. Notation: the symbol for the rooted trajectory expansion appears in several places without an explicit reference to its definition; adding a forward pointer on first use would eliminate minor ambiguity.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. No major comments appear in the report.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper states that its main inputs are the duality formulas from the companion paper and heat-kernel estimates from related works, but then explicitly carries out the construction of the rooted heat-kernel master loop equation on the extended decorated-loop space, the strong-coupling order-truncated rooted trajectory expansion, and the identification of the leading term with the master field. These steps are presented as independent mathematical content that produces the claimed infinite-volume limits, factorization, 1/N-expansion, and area-law bounds. No equation or claim in the provided text reduces by construction to a prior result (e.g., no fitted parameter renamed as prediction, no self-definitional closure, no uniqueness theorem imported solely to forbid alternatives). Self-citation of companion results is normal in a research program and does not meet the criteria for load-bearing circularity when the present manuscript supplies the new derivations and the results remain externally falsifiable via the stated estimates.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

The claim rests primarily on the validity of the companion paper's duality formulas and the cited estimates rather than deriving everything from first principles within this work.

axioms (3)
  • domain assumption Universal finite-N duality formulas from companion paper
    Main input used to derive the loop equation and expansion.
  • domain assumption Large-N heat-kernel estimates from cited papers
    Used for the strong-coupling analysis.
  • standard math Standard mathematical results on lattices and analysis
    Background for defining the model and proving convergence.

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Works this paper leans on

111 extracted references · 65 canonical work pages · 5 internal anchors

  1. [1]

    Avni, Nir and Glazer, Itay , TITLE =. Compos. Math. , FJOURNAL =. 2025 , NUMBER =. doi:10.1112/S0010437X24007644 , URL =

    work page doi:10.1112/s0010437x24007644 2025

  2. [2]

    Basu, Riddhipratim and Ganguly, Shirshendu , TITLE =. Comm. Pure Appl. Math. , FJOURNAL =. 2018 , NUMBER =. doi:10.1002/cpa.21788 , URL =

    work page doi:10.1002/cpa.21788 2018

  3. [3]

    Internat

    Blau, Matthias and Thompson, George , TITLE =. Internat. J. Modern Phys. A , FJOURNAL =. 1992 , NUMBER =. doi:10.1142/S0217751X9200168X , URL =

    work page doi:10.1142/s0217751x9200168x 1992

  4. [4]

    Benkart, Georgia and Chakrabarti, Manish and Halverson, Thomas and Leduc, Robert and Lee, Chanyoung and Stroomer, Jeffrey , TITLE =. J. Algebra , FJOURNAL =. 1994 , NUMBER =. doi:10.1006/jabr.1994.1166 , URL =

    work page doi:10.1006/jabr.1994.1166 1994

  5. [5]

    Surface sums for lattice

    Jacopo Borga and Sky Cao and Jasper Shogren-Knaak , year=. Surface sums for lattice. 2411.11676 , archivePrefix=

    work page arXiv

  6. [6]

    Cao, Sky and Park, Minjae and Sheffield, Scott , TITLE =. Commun. Am. Math. Soc. , FJOURNAL =. 2025 , PAGES =. doi:10.1090/cams/59 , URL =

    work page doi:10.1090/cams/59 2025

  7. [7]

    Cao, Sky and Chatterjee, Sourav , TITLE =. Comm. Math. Phys. , FJOURNAL =. 2024 , NUMBER =. doi:10.1007/s00220-023-04870-y , URL =

    work page doi:10.1007/s00220-023-04870-y 2024

  8. [8]

    Chatterjee, Sourav , TITLE =. Comm. Math. Phys. , FJOURNAL =. 2019 , NUMBER =. doi:10.1007/s00220-019-03353-3 , URL =

    work page doi:10.1007/s00220-019-03353-3 2019

  9. [9]

    Probability and analysis in interacting physical systems , SERIES =

    Chatterjee, Sourav , TITLE =. Probability and analysis in interacting physical systems , SERIES =. 2019 , MRCLASS =

    2019

  10. [10]

    Chevyrev, Ilya , TITLE =. Comm. Math. Phys. , FJOURNAL =. 2019 , NUMBER =. doi:10.1007/s00220-019-03567-5 , URL =

    work page doi:10.1007/s00220-019-03567-5 2019

  11. [11]

    Chevyrev, Ilya and Shen, Hao , TITLE =. Comm. Pure Appl. Math. , FJOURNAL =. 2026 , NUMBER =. doi:10.1002/cpa.70043 , URL =

    work page doi:10.1002/cpa.70043 2026

  12. [12]

    Chevyrev, Ilya and Shen, Hao , TITLE =. Arch. Ration. Mech. Anal. , FJOURNAL =. 2026 , NUMBER =. doi:10.1007/s00205-025-02163-3 , URL =

    work page doi:10.1007/s00205-025-02163-3 2026

  13. [13]

    Chandra, Ajay and Chevyrev, Ilya and Hairer, Martin and Shen, Hao , TITLE =. Publ. Math. Inst. Hautes \'. 2022 , PAGES =. doi:10.1007/s10240-022-00132-0 , URL =

    work page doi:10.1007/s10240-022-00132-0 2022

  14. [14]

    Chandra, Ajay and Chevyrev, Ilya and Hairer, Martin and Shen, Hao , TITLE =. Invent. Math. , FJOURNAL =. 2024 , NUMBER =. doi:10.1007/s00222-024-01264-2 , URL =

    work page doi:10.1007/s00222-024-01264-2 2024

  15. [15]

    Chevyrev, Ilya and Garban, Christophe , TITLE =. J. Stat. Phys. , FJOURNAL =. 2025 , NUMBER =. doi:10.1007/s10955-025-03420-1 , URL =

    work page doi:10.1007/s10955-025-03420-1 2025

  16. [16]

    https://doi.org/10.1007/s00220-006-1554-3 Christoph Dankert, Richard Cleve, Joseph Emerson, and Etera Livine

    Collins, Beno\^. Integration with respect to the. Comm. Math. Phys. , FJOURNAL =. 2006 , NUMBER =. doi:10.1007/s00220-006-1554-3 , URL =

    work page doi:10.1007/s00220-006-1554-3 2006

  17. [17]

    Generalized Lattice Gauge Theory, Spin Foams and State Sum Invariants

    Robert Oeckl , title =. Journal of Geometry and Physics , volume =. 2003 , doi =. hep-th/0110259 , archivePrefix=

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  18. [18]

    2005 , eprint =

    Florian Conrady , title =. 2005 , eprint =

    2005

  19. [19]

    Dual Computations of Non-abelian Yang-Mills on the Lattice

    J. Wade Cherrington and J. Daniel Christensen and Igor Khavkine , title =. Physical Review D , volume =. 2007 , doi =. 0705.2629 , archivePrefix=

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  20. [20]

    International Mathematics Research Notices2003, 17 (2003), 953–982

    Collins, Beno\^. Moments and cumulants of polynomial random variables on unitary groups, the. Int. Math. Res. Not. , FJOURNAL =. 2003 , NUMBER =. doi:10.1155/S107379280320917X , URL =

    work page doi:10.1155/s107379280320917x 2003

  21. [21]

    Cordes, Stefan and Moore, Gregory and Ramgoolam, Sanjaye , TITLE =. Comm. Math. Phys. , FJOURNAL =. 1997 , NUMBER =. doi:10.1007/s002200050102 , URL =

    work page doi:10.1007/s002200050102 1997

  22. [22]

    Cox, Anton and De Visscher, Maud and Doty, Stephen and Martin, Paul , TITLE =. J. Algebra , FJOURNAL =. 2008 , NUMBER =. doi:10.1016/j.jalgebra.2008.01.026 , URL =

    work page doi:10.1016/j.jalgebra.2008.01.026 2008

  23. [23]

    Dahlqvist, Antoine , TITLE =. Ann. Inst. Henri Poincar\'. 2017 , NUMBER =. doi:10.1214/16-AIHP779 , URL =

    work page doi:10.1214/16-aihp779 2017

  24. [24]

    Dahlqvist, Antoine , TITLE =. Comm. Math. Phys. , FJOURNAL =. 2016 , NUMBER =. doi:10.1007/s00220-016-2756-y , URL =

    work page doi:10.1007/s00220-016-2756-y 2016

  25. [25]

    2603.11374 , archivePrefix=

    Antoine Dahlqvist , year=. 2603.11374 , archivePrefix=

    work page arXiv

  26. [26]

    Forum Math

    Dahlqvist, Antoine and Lemoine, Thibaut , TITLE =. Forum Math. Sigma , FJOURNAL =. 2025 , PAGES =. doi:10.1017/fms.2024.152 , URL =

    work page doi:10.1017/fms.2024.152 2025

  27. [27]

    Dahlqvist, Antoine and Lemoine, Thibaut , TITLE =. Probab. Math. Phys. , FJOURNAL =. 2023 , NUMBER =

    2023

  28. [28]

    , TITLE =

    Dahlqvist, Antoine and Norris, James R. , TITLE =. Comm. Math. Phys. , FJOURNAL =. 2020 , NUMBER =. doi:10.1007/s00220-020-03773-6 , URL =

    work page doi:10.1007/s00220-020-03773-6 2020

  29. [29]

    Nguyen Viet Dang and Elias Nohra , year=. The. 2602.08591 , archivePrefix=

    work page arXiv

  30. [30]

    Decorated tensor network renormalization for lattice gauge theories and spin foam models

    Bianca Dittrich and Sebastian Mizera and Sebastian Steinhaus , title =. New Journal of Physics , volume =. 2016 , doi =. 1409.2407 , archivePrefix=

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  31. [31]

    , TITLE =

    Driver, Bruce K. , TITLE =. Comm. Math. Phys. , FJOURNAL =. 1989 , NUMBER =

    1989

  32. [32]

    and Hall, Brian C

    Driver, Bruce K. and Hall, Brian C. and Kemp, Todd , TITLE =. J. Funct. Anal. , FJOURNAL =. 2013 , NUMBER =. doi:10.1016/j.jfa.2013.07.020 , URL =

    work page doi:10.1016/j.jfa.2013.07.020 2013

  33. [33]

    and Hall, Brian C

    Driver, Bruce K. and Hall, Brian C. and Kemp, Todd , TITLE =. Comm. Math. Phys. , FJOURNAL =. 2017 , NUMBER =. doi:10.1007/s00220-016-2793-6 , URL =

    work page doi:10.1007/s00220-016-2793-6 2017

  34. [34]

    and Gabriel, Franck and Hall, Brian C

    Driver, Bruce K. and Gabriel, Franck and Hall, Brian C. and Kemp, Todd , TITLE =. Comm. Math. Phys. , FJOURNAL =. 2017 , NUMBER =. doi:10.1007/s00220-017-2857-2 , URL =

    work page doi:10.1007/s00220-017-2857-2 2017

  35. [35]

    , TITLE =

    Fegan, Howard D. , TITLE =. 1991 , PAGES =. doi:10.1142/1436 , URL =

    work page doi:10.1142/1436 1991

  36. [36]

    Forman, Robin , TITLE =. Comm. Math. Phys. , FJOURNAL =. 1993 , NUMBER =

    1993

  37. [37]

    2025 , eprint=

    Traceless projection of mixed tensor products, and walled Brauer algebras , author=. 2025 , eprint=

    2025

  38. [38]

    and Taylor, IV, Washington , TITLE =

    Gross, David J. and Taylor, IV, Washington , TITLE =. Nuclear Phys. B , FJOURNAL =. 1993 , NUMBER =

    1993

  39. [39]

    , TITLE =

    Hall, Brian C. , TITLE =. Comm. Math. Phys. , FJOURNAL =. 2018 , NUMBER =. doi:10.1007/s00220-018-3262-1 , URL =

    work page doi:10.1007/s00220-018-3262-1 2018

  40. [40]

    Pacific J

    Halverson, Tom , TITLE =. Pacific J. Math. , FJOURNAL =. 1996 , NUMBER =

    1996

  41. [41]

    A Planar Diagram Theory for Strong Interactions

    't Hooft, Gerard. A Planar Diagram Theory for Strong Interactions. Nucl. Phys. B. 1974

    1974

  42. [42]

    Wilson loop expectations in $SU(N)$ lattice gauge theory

    Jafar Jafarov , year=. Wilson loop expectations in. 1610.03821 , archivePrefix=

    work page internal anchor Pith review Pith/arXiv arXiv

  43. [43]

    The millennium prize problems , PAGES =

    Jaffe, Arthur and Witten, Edward , TITLE =. The millennium prize problems , PAGES =. 2006 , MRCLASS =

    2006

  44. [44]

    and Kirwan, Frances C

    Jeffrey, Lisa C. and Kirwan, Frances C. , TITLE =. Ann. of Math. (2) , FJOURNAL =. 1998 , NUMBER =. doi:10.2307/120993 , URL =

    work page doi:10.2307/120993 1998

  45. [45]

    Kimura, Yusuke and Ramgoolam, Sanjaye , TITLE =. J. High Energy Phys. , FJOURNAL =. 2007 , NUMBER =. doi:10.1088/1126-6708/2007/11/078 , URL =

    work page doi:10.1088/1126-6708/2007/11/078 2007

  46. [46]

    Kimura, Yusuke and Ramgoolam, Sanjaye , TITLE =. J. High Energy Phys. , FJOURNAL =. 2008 , NUMBER =. doi:10.1088/1126-6708/2008/06/015 , URL =

    work page doi:10.1088/1126-6708/2008/06/015 2008

  47. [47]

    Koike, Kazuhiko , TITLE =. Adv. Math. , FJOURNAL =. 1989 , NUMBER =. doi:10.1016/0001-8708(89)90004-2 , URL =

    work page doi:10.1016/0001-8708(89)90004-2 1989

  48. [48]

    Littlewood, D. E. , TITLE =. Philos. Trans. Roy. Soc. London Ser. A , FJOURNAL =. 1944 , PAGES =

    1944

  49. [49]

    Lemoine, Thibaut , TITLE =. Combin. Probab. Comput. , FJOURNAL =. 2022 , NUMBER =. doi:10.1017/s0963548321000262 , URL =

    work page doi:10.1017/s0963548321000262 2022

  50. [51]

    Universal dualities for Wilson loops in lattice Yang-Mills

    Thibaut Lemoine , year=. Universal dualities for. 2604.16252 , archivePrefix=

    work page internal anchor Pith review Pith/arXiv arXiv

  51. [52]

    Lemoine, Thibaut , title = "Almost flat highest weights and application to. Probab. Theory Related Fields , FJOURNAL =. 2025 , primaryClass=

    2025

  52. [53]

    Two-dimensional

    Thibaut Lemoine , year=. Two-dimensional. Bull. Amer. Soc. , note=. 2508.16162 , archivePrefix=

    work page arXiv

  53. [54]

    Gaussian measure on the dual of

    Lemoine, Thibaut and Ma\". Gaussian measure on the dual of. Ann. Probab. , FJOURNAL =. 2025 , NUMBER =. doi:10.1214/24-aop1749 , URL =

    work page doi:10.1214/24-aop1749 2025

  54. [55]

    2025 , eprint=

    The central heat trace on large compact classical groups , author=. 2025 , eprint=

    2025

  55. [56]

    L. Yang-. Mem. Amer. Math. Soc. , FJOURNAL =. 2003 , NUMBER =. doi:10.1090/memo/0790 , URL =

    work page doi:10.1090/memo/0790 2003

  56. [57]

    L. Schur-. Adv. Math. , FJOURNAL =. 2008 , NUMBER =

    2008

  57. [58]

    Two-dimensional

    L. Two-dimensional. Ast\'. 2010 , PAGES =

    2010

  58. [59]

    The master field on the plane , JOURNAL =

    L. The master field on the plane , JOURNAL =. 2017 , PAGES =

    2017

  59. [60]

    Two-dimensional quantum

    L. Two-dimensional quantum. Frontiers in analysis and probability---in the spirit of the. 2020 , MRCLASS =

    2020

  60. [61]

    Four chapters on low-dimensional gauge theories , BOOKTITLE =

    L. Four chapters on low-dimensional gauge theories , BOOKTITLE =. 2017 , MRCLASS =

    2017

  61. [62]

    2026 , note=

    Lemoine, Thibaut and Nohra, Elias , title =. 2026 , note=

    2026

  62. [63]

    A combinatorial formula for

    L. A combinatorial formula for. 2026 , eprint=

    2026

  63. [64]

    Large deviations for the

    L. Large deviations for the. Comm. Math. Phys. , FJOURNAL =. 2006 , NUMBER =. doi:10.1007/s00220-005-1450-2 , URL =

    work page doi:10.1007/s00220-005-1450-2 2006

  64. [65]

    Liu, Kefeng , TITLE =. Math. Res. Lett. , FJOURNAL =. 1996 , NUMBER =. doi:10.4310/MRL.1996.v3.n6.a3 , URL =

    work page doi:10.4310/mrl.1996.v3.n6.a3 1996

  65. [66]

    Magee, Michael , TITLE =. Comm. Math. Phys. , FJOURNAL =. 2022 , NUMBER =

    2022

  66. [67]

    Magee, Michael , TITLE =. Geom. Topol. , FJOURNAL =. 2025 , NUMBER =

    2025

  67. [68]

    Magee, Michael and de la Salle, Mikael , TITLE =. Geom. Funct. Anal. , FJOURNAL =. 2026 , NUMBER =. doi:10.1007/s00039-026-00730-8 , URL =

    work page doi:10.1007/s00039-026-00730-8 2026

  68. [69]

    Magee, Michael and Puder, Doron , TITLE =. Invent. Math. , FJOURNAL =. 2019 , NUMBER =. doi:10.1007/s00222-019-00891-4 , URL =

    work page doi:10.1007/s00222-019-00891-4 2019

  69. [70]

    , TITLE =

    Meinrenken, E. , TITLE =. Adv. Math. , FJOURNAL =. 2005 , NUMBER =. doi:10.1016/j.aim.2004.10.002 , URL =

    work page doi:10.1016/j.aim.2004.10.002 2005

  70. [71]

    Recursion Equations in Gauge Theories

    Migdal, Alexander A. Recursion Equations in Gauge Theories. Sov. Phys. JETP. 1975

    1975

  71. [72]

    Mirzakhani, Maryam , TITLE =. Invent. Math. , FJOURNAL =. 2007 , NUMBER =. doi:10.1007/s00222-006-0013-2 , URL =

    work page doi:10.1007/s00222-006-0013-2 2007

  72. [73]

    On the 2D

    Jonathan Novak , year=. On the 2D. 2401.00628 , archivePrefix=

    work page arXiv

  73. [74]

    Rusakov, B. Ye. , TITLE =. Modern Phys. Lett. A , FJOURNAL =. 1990 , NUMBER =. doi:10.1142/S0217732390000780 , URL =

    work page doi:10.1142/s0217732390000780 1990

  74. [75]

    Nuclear Phys

    Oeckl, Robert and Pfeiffer, Hendryk , TITLE =. Nuclear Phys. B , FJOURNAL =. 2001 , NUMBER =. doi:10.1016/S0550-3213(00)00770-7 , URL =

    work page doi:10.1016/s0550-3213(00)00770-7 2001

  75. [76]

    Sengupta, Ambar , TITLE =. Mem. Amer. Math. Soc. , FJOURNAL =. 1997 , NUMBER =. doi:10.1090/memo/0600 , URL =

    work page doi:10.1090/memo/0600 1997

  76. [77]

    Sengupta, Ambar , TITLE =. Comm. Math. Phys. , FJOURNAL =. 1997 , NUMBER =. doi:10.1007/s002200050047 , URL =

    work page doi:10.1007/s002200050047 1997

  77. [78]

    , TITLE =

    Sengupta, Ambar N. , TITLE =. Traces in number theory, geometry and quantum fields , SERIES =. 2008 , ISBN =

    2008

  78. [79]

    and Zhu, Rongchan , TITLE =

    Shen, Hao and Smith, Scott A. and Zhu, Rongchan , TITLE =. Electron. J. Probab. , FJOURNAL =. 2024 , PAGES =. doi:10.1214/24-ejp1090 , URL =

    work page doi:10.1214/24-ejp1090 2024

  79. [80]

    Smith and Rongchan Zhu , year=

    Hao Shen and Scott A. Smith and Rongchan Zhu , year=. 2412.15422 , archivePrefix=

    work page arXiv

  80. [81]

    2512.00570 , archivePrefix=

    Hao Shen and Scott Andrew Smith and Rongchan Zhu , year=. 2512.00570 , archivePrefix=

    work page arXiv

Showing first 80 references.