Paper Citation Record · LEDGER

Propagation of chaos and approximation error of random batch particle system in the mean field regime

As of 16 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 1 inbound Pith citation observation for arXiv:2505.12172.

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pith.paper-citation-record.v1
2505.12172 v1

Coverage vector

measured 46 of 46 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T20:51:04.498411Z

measured 47 of 47 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T14:43:41.647149Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-15T14:43:41.945643Z

Reference resolution

46 of 46 outbound references displayed

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External citation measurements

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Outbound references

Observation 9a678e1d-649d-4b86-bb28-286532b4ac7b · outbound

This paper cites Characterization of radially symmetric finite time blowup in multidimensional aggregation equations.SIAM Journal on Mathematical Analysis, 44(2):651–681, 2012.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Characterization of radially symmetric finite time blowup in multidimensional aggregation equations.SIAM Journal on Mathematical Analysis, 44(2):651–681, 2012

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:05.384390Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 0cfe2a1c-1753-4c9f-b017-566364fe8aa0 · outbound

This paper cites A duality method for mean-field limits with singular interactions.

Propagation of chaos and approximation error of random batch particle system in the mean field regime A duality method for mean-field limits with singular interactions

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-15T20:51:04.299915Z

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Observation 73bd8daf-30af-4b72-95be-6cdf8604f29d · outbound

This paper cites Biology of synchronous flashing of fireflies, 1966.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Biology of synchronous flashing of fireflies, 1966

Reference 3

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Observation 777ca186-2aa0-4d81-9136-05dec3e25d0f · outbound

This paper cites Random batch particle methods for the homogeneous Landau equation.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Random batch particle methods for the homogeneous Landau equation

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-15T20:51:04.716949Z

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Observation aaa9704f-4a36-483e-b326-4a2d443313d7 · outbound

This paper cites Entropy on the path space and application to singular diffusions and mean-field models.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Entropy on the path space and application to singular diffusions and mean-field models

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-15T20:51:04.315008Z

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Observation 594b2260-da83-47e5-8316-cb2bb44a6ba5 · outbound

This paper cites Propagation of chaos: a review of models, methods and applications. I. Models and methods.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Propagation of chaos: a review of models, methods and applications. I. Models and methods

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-15T20:51:04.319933Z

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Observation ac6e5db1-c152-4442-a467-d1979605cdbd · outbound

This paper cites Propagation of chaos: a review of models, methods and applications. II. Applications.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Propagation of chaos: a review of models, methods and applications. II. Applications

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-15T20:51:04.326037Z

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Observation 1ed49aa2-ca66-4b7c-98a6-ab0a94478805 · outbound

This paper cites Sanov property, generalized i-projection and a conditional limit theorem.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Sanov property, generalized i-projection and a conditional limit theorem

Reference 8

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Observation 95e1ba3b-db1c-4bf1-bb25-04911499a502 · outbound

This paper cites Emergent behavior in flocks.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Emergent behavior in flocks

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:05.344989Z

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Observation 71c4284c-e1c2-4795-b948-40e5e884a8af · outbound

This paper cites A collision-oriented interacting particle system for Landau-type equations and the molecular chaos.

Propagation of chaos and approximation error of random batch particle system in the mean field regime A collision-oriented interacting particle system for Landau-type equations and the molecular chaos

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-15T20:51:04.338953Z

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Observation 2c766f12-9142-4e45-bd9b-1763c8f116b8 · outbound

This paper cites Rbmd: A molecular dynamics package enabling to simulate 10 million all-atom particles in a single graphics processing unit.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Rbmd: A molecular dynamics package enabling to simulate 10 million all-atom particles in a single graphics processing unit

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-15T20:51:04.343688Z

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Unavailable: canonical work link unavailable.

Observation 6c11860a-1202-40bc-889c-ba74ec6f0c0d · outbound

This paper cites On the dynamics of large particle systems in the mean field limit.

Propagation of chaos and approximation error of random batch particle system in the mean field regime On the dynamics of large particle systems in the mean field limit

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:05.330289Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4dcf3899-fc79-4705-b620-f9eb9f5bfc64 · outbound

This paper cites Sharp propagation of chaos for McKean-Vlasov equation with non constant diffusion coefficient.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Sharp propagation of chaos for McKean-Vlasov equation with non constant diffusion coefficient

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-15T20:51:04.352428Z

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Observation 9d698d15-9adb-4247-a168-1fb52c7e03c5 · outbound

This paper cites Uniform-in-time error estimate of the random batch method for the Cucker–Smale model.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Uniform-in-time error estimate of the random batch method for the Cucker–Smale model

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:05.315672Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 78507b4d-2b7f-45ac-83ef-bdb591f2dccb · outbound

This paper cites A simple proof of the cucker-smale flocking dynamics and mean-field limit.

Propagation of chaos and approximation error of random batch particle system in the mean field regime A simple proof of the cucker-smale flocking dynamics and mean-field limit

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:05.300388Z

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Observation d2897966-8449-44c6-9f04-b6362e7703f7 · outbound

This paper cites From particle to kinetic and hydrodynamic descrip- tions of flocking.

Propagation of chaos and approximation error of random batch particle system in the mean field regime From particle to kinetic and hydrodynamic descrip- tions of flocking

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:05.283563Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c48e6490-aae4-4225-8a78-5fcc068a1c7e · outbound

This paper cites Strong convergence of propagation of chaos for McKean–Vlasov SDEs with singular interactions.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Strong convergence of propagation of chaos for McKean–Vlasov SDEs with singular interactions

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:05.167986Z

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Observation 68fd40ff-29ea-4d3b-a810-e0cbb85e93f0 · outbound

This paper cites From 1970 until present : the Keller-Segel model in chemotaxis and its consequences I.

Propagation of chaos and approximation error of random batch particle system in the mean field regime From 1970 until present : the Keller-Segel model in chemotaxis and its consequences I

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:05.152448Z

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Observation f8dac1b8-b4a0-44c6-83b5-bc213bb6f220 · outbound

This paper cites Mean field error estimate of the random batch method for large interacting particle system.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Mean field error estimate of the random batch method for large interacting particle system

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:05.137716Z

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Observation ed456a31-851e-4c49-9960-2aea2cf23d0b · outbound

This paper cites A review of the mean field limits for Vlasov equations.

Propagation of chaos and approximation error of random batch particle system in the mean field regime A review of the mean field limits for Vlasov equations

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:05.124376Z

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Observation 37b80f81-d84e-416e-bc40-3f0fefddf647 · outbound

This paper cites Mean field limit and propagation of chaos for Vlasov systems with bounded forces.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Mean field limit and propagation of chaos for Vlasov systems with bounded forces

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:05.110937Z

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Observation 47ee126d-067a-4aab-a405-ed7a995c3f1f · outbound

This paper cites Mean field limit for stochastic particle systems.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Mean field limit for stochastic particle systems

Reference 22

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d0c1ffd1-6d8a-4735-a149-934f3fd701cf · outbound

This paper cites Quantitative estimates of propagation of chaos for stochastic systems with W−1,∞ kernels.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Quantitative estimates of propagation of chaos for stochastic systems with W−1,∞ kernels

Reference 23

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Observation 6864c4cf-ac22-435b-a270-2bf94178632e · outbound

This paper cites Random batch methods for classical and quantum interacting particle systems and statistical samplings.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Random batch methods for classical and quantum interacting particle systems and statistical samplings

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:05.066039Z

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Observation 0ff57def-ef49-45a5-89fb-dcbdad869bb0 · outbound

This paper cites On the mean field limit of the Random Batch Method for interacting particle systems.

Propagation of chaos and approximation error of random batch particle system in the mean field regime On the mean field limit of the Random Batch Method for interacting particle systems

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:05.050318Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation fc5e75b7-2b3e-4a73-adde-06ee23a3c06d · outbound

This paper cites Random batch methods (rbm) for interacting particle systems.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Random batch methods (rbm) for interacting particle systems

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:05.035594Z

Source-reported events for the cited work

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Observation 4d6ff243-2642-4075-bffb-c845d4b06520 · outbound

This paper cites On the Random Batch Method for second order interacting particle systems.

Propagation of chaos and approximation error of random batch particle system in the mean field regime On the Random Batch Method for second order interacting particle systems

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:05.019973Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 813f6669-d331-49f6-be40-4a9001bd5a29 · outbound

This paper cites A random batch Ewald method for par- ticle systems with Coulomb interactions.

Propagation of chaos and approximation error of random batch particle system in the mean field regime A random batch Ewald method for par- ticle systems with Coulomb interactions

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:05.004320Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation b5366a59-bfd6-41c3-85ce-ceb268365a0e · outbound

This paper cites Ergodicity and long-time behavior of the random batch method for interacting particle systems.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Ergodicity and long-time behavior of the random batch method for interacting particle systems

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:04.987853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 6f43224b-9291-4113-bd52-2aaeb04ec76c · outbound

This paper cites Random Batch Algorithms for Quantum Monte Carlo simulations.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Random Batch Algorithms for Quantum Monte Carlo simulations

Reference 30

Resolution: verified exact; local_arxiv, observed 2026-08-15T20:51:04.540544Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e3c2c166-d1c8-473e-a214-fa6198350569 · outbound

This paper cites Foundations of kinetic theory.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Foundations of kinetic theory

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:04.972227Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8b017b67-be1d-48f3-864e-bbe6cf7e96e7 · outbound

This paper cites Self-entrainment of a population of coupled non-linear oscillators.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Self-entrainment of a population of coupled non-linear oscillators

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:04.955268Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d15e0c64-cc3c-4467-9d1d-f1c225d6b0fb · outbound

This paper cites Hierarchies, entropy, and quantitative propagation of chaos for mean field diffusions.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Hierarchies, entropy, and quantitative propagation of chaos for mean field diffusions

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:04.939983Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation af2ab966-f81b-4cc6-8306-9854966fa49f · outbound

This paper cites Sharp uniform-in-time propagation of chaos.Probability Theory and Related Fields , 187(1-2):443–480, 2023.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Sharp uniform-in-time propagation of chaos.Probability Theory and Related Fields , 187(1-2):443–480, 2023

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:04.922239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a5e5fccf-9c3f-4bce-b51b-30c4e3ae7ae8 · outbound

This paper cites Some Random Batch Particle Methods for the Poisson-Nernst-Planck and Poisson-Boltzmann Equations.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Some Random Batch Particle Methods for the Poisson-Nernst-Planck and Poisson-Boltzmann Equations

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:04.905649Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c2a43da7-f049-4eb2-a06d-20b26e784c0a · outbound

This paper cites A random-batch Monte Carlo method for many-body systems with singular kernels.

Propagation of chaos and approximation error of random batch particle system in the mean field regime A random-batch Monte Carlo method for many-body systems with singular kernels

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:04.887006Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 2b617791-f035-42ff-8707-6109fb25214d · outbound

This paper cites Su- perscalability of the random batch Ewald method.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Su- perscalability of the random batch Ewald method

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:04.869734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f3af2cd6-4a60-4d07-a03d-a0af918ca71e · outbound

This paper cites Vorticity and incompressible flow.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Vorticity and incompressible flow

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:04.853804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 6739df37-bb07-44dc-9fea-460f4fd22b6b · outbound

This paper cites Genealogies and increasing propagation of chaos for feynman-kac and genetic models.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Genealogies and increasing propagation of chaos for feynman-kac and genetic models

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:04.837296Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8782551b-7f2e-43ec-a59e-87abff486489 · outbound

This paper cites A new model for self-organized dynamics and its flocking behavior.

Propagation of chaos and approximation error of random batch particle system in the mean field regime A new model for self-organized dynamics and its flocking behavior

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:04.821447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 75981de3-de1a-47b7-a803-59d8bd0c29a5 · outbound

This paper cites Heterophilious dynamics enhances consensus.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Heterophilious dynamics enhances consensus

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-15T20:51:04.477702Z

Source-reported events for the cited work

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Observation ce71f1f8-eb36-4000-ae35-52ab894dca07 · outbound

This paper cites Information and information stability of random variables and pro- cesses.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Information and information stability of random variables and pro- cesses

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:04.795922Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e975737d-2adc-474e-8f7e-88b05603317c · outbound

This paper cites Flocks, herds, and schools: A quantitative theory of flocking.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Flocks, herds, and schools: A quantitative theory of flocking

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-15T20:51:04.485833Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 59809023-aa65-43ac-9211-5bbb4dcbfd6c · outbound

This paper cites High-dimensional probability: An introduction with applications in data science, volume 47.

Propagation of chaos and approximation error of random batch particle system in the mean field regime High-dimensional probability: An introduction with applications in data science, volume 47

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-15T20:51:04.490073Z

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Observation 5eda1fba-d1a0-4b10-ade4-229a4338cd89 · outbound

This paper cites Springer, 2009.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Springer, 2009

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-15T20:51:04.494286Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a0ac609d-0096-4316-8d82-e45f01f06ba1 · outbound

This paper cites Error analysis of time-discrete random batch method for interacting particle systems and associated mean-field limits.IMA Journal of Numerical Analysis, 44(3):1660–1698, 2024.

Propagation of chaos and approximation error of random batch particle system in the mean field regime Error analysis of time-discrete random batch method for interacting particle systems and associated mean-field limits.IMA Journal of Numerical Analysis, 44(3):1660–1698, 2024

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:51:04.750039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Pith citing papers

Observation d8b99092-a67f-43aa-9cde-def58030e5cb · inbound

Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation cites this paper.

Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Propagation of chaos and approximation error of random batch particle system in the mean field regime

Reference 41

Resolution: verified exact; local_arxiv, observed 2026-08-15T14:43:41.953071Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.