Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T14:43:41.902858Z
Paper Citation Record · LEDGER
As of 16 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 0 inbound Pith citation observations for arXiv:2608.06533.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T14:43:41.902858Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
51 of 51 outbound references displayed
External citation measurements
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Observation 69d6abf1-b6a0-42da-9d48-44c52ad7d13b · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Thomas Beale and Andrew Majda
Reference 1
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 f2a27801-4bad-47c7-8d0a-8cddb4f2ada6 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Thomas Beale and Andrew Majda
Reference 2
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 b29d33b8-e2e7-41a1-b5bc-ed86643d6492 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Global solutions of two-dimensional Navier-Stokes and Euler equations
Reference 3
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 b492096b-6f5a-45f4-b690-912f1ee16497 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Berselli and Stefano Spirito
Reference 4
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 1029106a-d0a7-42f1-a09e-8e876476ef75 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Weighted Csisz´ ar-Kullback-Pinsker inequalities and ap- plications to transportation inequalities
Reference 5
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 9992bf61-26a6-4ef8-8274-f9ce77d318f1 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Convergence of random batch method with replacement for interacting particle systems.Mathematics of Computation, 2026
Reference 6
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 3935f0eb-0ba5-4594-82ef-152ee53ec1df · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Carrillo, Shi Jin, Lei Li, and Yuhua Zhu
Reference 7
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 a257a1ba-fbdd-4f50-90ef-0bb4dee374cf · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Carrillo, Shi Jin, and Yijia Tang
Reference 8
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 6f4a4a67-c674-4d18-acc0-1f5c7c163d93 · outbound
Reference 9
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 b3776079-53a3-4f8e-87f8-f0d8cf8989d6 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Unresolved cited work
Reference 10
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 04c2da18-c7bb-4738-8a05-bd8157c9d183 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation A blob method for the aggregation equation.Mathematics of Computation, 85(300):1681–1717, 2016
Reference 11
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 2668fcc4-61d6-4af9-8602-ca0b9ba3f0f8 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation A collision-oriented interacting particle system for Landau-type equations and the molecular chaos
Reference 12
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ae13715b-4bb3-4d5a-bbf4-bb996737c33f · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation A structure-preserving collisional particle method for the Landau kinetic equation.Journal of Computational Physics, 543:114387, 2025
Reference 13
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 545d77c3-791c-4c66-99c9-878a14044391 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Quantitative propagation of chaos for 2D viscous vortex model on the whole space.Peking Mathematical Journal, 2026
Reference 14
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 89ec95f4-7994-4ed1-95db-27221dc55cc0 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Quantitative propagation of chaos for 2D viscous vortex model with general circulations on the whole space.Nonlinearity, 39(1):015009, 2026
Reference 15
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 5d9d8533-aff4-4fe4-ba8b-fb3243973b0b · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Propagation of chaos for the 2D viscous vortex model.Journal of the European Mathematical Society, 16(7):1423–1466, 2014
Reference 16
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 030dc712-13b8-49f6-9e34-cb14913be959 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation On the dynamics of large particle systems in the mean field limit
Reference 17
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 5d195631-b102-4c1a-9c76-b6508320b8e2 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation The random batch method forN-body quantum dynamics.Journal of Computational Mathematics, 39(6):897–922, 2021
Reference 18
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 55a8a505-4cf2-4d44-8040-c6814bee438a · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Convergence of the random vortex method.Communications on Pure and Applied Mathematics, 40(2):189–220, 1987
Reference 19
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 cb237dde-7622-4008-9b97-bc6c12f9d857 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Hou, and John Lowengrub
Reference 20
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 a6229a45-895d-4c9a-b02d-1d7570d08390 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Tinsley Oden, and Serge Prudhomme
Reference 21
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 e03f62f8-7a9f-4511-975b-13a77c3a28d3 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Uniform in time propagation of chaos for the 2D vortex model and other singular stochastic systems.Journal of the European Mathematical Society, 27(6):2359–2386, 2025
Reference 22
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 56540ef7-39b4-4a6d-9783-f5c8bf86fd39 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Uniform-in-time error estimate of the random batch method for the Cucker–Smale model.Mathematical Models and Methods in Applied Sciences, 31(6):1099–1135, 2021
Reference 23
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 e0beba17-7d8d-4204-afe1-269d69bc9bdc · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Unresolved cited work
Reference 24
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 8e2e94d9-8654-465f-943b-3622d4b909bd · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Hou and John Lowengrub
Reference 25
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 2fba1f81-b124-48af-addb-cb25a43f650e · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Mean field error estimate of the random batch method for large interacting particle system.ESAIM: Mathematical Modelling and Numerical Analysis, 59(1):265–289, 2025
Reference 26
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 1b4f5026-5911-4e5a-b572-50bde2363666 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation A review of the mean field limits for Vlasov equations.Kinetic and Related Models, 7(4):661–711, 2014
Reference 27
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 2311d8cd-f8fa-4f0c-8ec7-70d94df58a81 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Mean field limit for stochastic particle systems
Reference 28
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 738c3c2c-9935-4ec5-b9a7-26023c37cc2b · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Quantitative estimates of propagation of chaos for stochastic systems withW −1,∞ kernels.Inventiones Mathematicae, 214(1):523–591, 2018
Reference 29
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 1b35fc14-6034-48af-9aa7-2202d1fcc82b · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation On the mean field limit of the random batch method for interacting particle systems.Science China Mathematics, 65(1):169–202, 2022
Reference 30
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 0c0a6de4-7471-4a1b-80ae-cdd87c06808a · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Random batch methods (RBM) for interacting particle systems.Journal of Computational Physics, 400:108877, 2020
Reference 31
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 9d56a084-0dd1-4a6d-926e-b7b206ff59e1 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Convergence of the random batch method for interacting particles with disparate species and weights.SIAM Journal on Numerical Analysis, 59(2):746– 768, 2021
Reference 32
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 662da9a7-96b8-423d-8f9a-bc2b8ccf6dfe · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation On the random batch method for second-order interacting particle systems.Multiscale Modeling & Simulation, 20(2):741–768, 2022
Reference 33
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 3de5b3cb-93c7-4db1-93b2-b026532e812e · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation A random batch Ewald method for particle systems with Coulomb interactions.SIAM Journal on Scientific Computing, 43(4):B937–B960, 2021
Reference 34
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 c2f3086d-e7fc-42c1-a332-de6affb1924c · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Ergodicity and long-time behavior of the random batch method for interacting particle systems.Mathematical Models and Methods in Applied Sciences, 33(1):67–102, 2023
Reference 35
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 b2eb2a5a-425f-4793-bf05-fe8c53eb958f · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Random batch algorithms for quantum Monte Carlo simulations
Reference 36
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 da45c77e-6bf0-40f9-a9c2-daa30659fa34 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Asymptotic uniform estimate of random batch method with replacement for the Cucker–Smale model.Mathematical Models and Methods in Applied Sciences, pages 1–57, 2026
Reference 37
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 cf1abe97-a090-4005-86c6-44755a7321e6 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Sur le mouvement d’un liquide visqueux emplissant l’espace.Acta Mathematica, 63:193–248, 1934
Reference 38
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 3b81d040-6927-4f38-90de-7ca5a1026a15 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation A stochastic version of Stein variational gradient descent for efficient sampling.Communications in Applied Mathematics and Computational Science, 15(1):37–63, 2020
Reference 39
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 f41c1b9d-c41f-421b-bf94-55a49b056de0 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Some random batch particle methods for the Poisson– Nernst–Planck and Poisson–Boltzmann equations.Communications in Computational Physics, 32(1):41–82, 2022
Reference 40
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 d8b99092-a67f-43aa-9cde-def58030e5cb · outbound
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
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 b947e4a9-2b34-44a6-8803-b3f4a18871ed · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation A random-batch Monte Carlo method for many-body systems with singular kernels.SIAM Journal on Scientific Computing, 42(3):A1486–A1509, 2020
Reference 42
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 0fe015b7-bbba-4857-93c7-0b5ba67e5f09 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Superscalability of the random batch Ewald method.The Journal of Chemical Physics, 156(1):014114, 2022
Reference 43
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 a0261a12-38ad-4614-9a1e-fa4244ac89e0 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation On random batch methods (RBM) for interacting particle systems driven by L´ evy processes.Stochastics and Dynamics, 25(7–8):2550034, 2025
Reference 44
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 a428f4e7-ab2f-44ac-95ca-ed13eda81cd8 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Convergence of vortex methods for weak solutions to the 2-D Euler equations with vortex sheet data.Communications on Pure and Applied Mathematics, 48(6):611–628, 1995
Reference 45
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 6548658b-88f9-4dd9-92c6-8f78c7e40481 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Convergence of the random vortex method in two dimensions.Journal of the American Mathematical Society, 1(4):779–804, 1988
Reference 46
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 3f6067f0-41d2-4f08-9516-7fd74879598e · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Hydrodynamics in two dimensions and vortex theory
Reference 47
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 bf5a8b14-6465-42d1-ace1-af1480ce181e · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Propagation of chaos for the two-dimensional Navier–Stokes equation.Pro- ceedings of the Japan Academy, Series A, Mathematical Sciences, 62(1):8–11, 1986
Reference 48
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 2abcdfb6-d488-4589-9e3a-0c7f39a72908 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation Propagation of chaos for the two-dimensional Navier–Stokes equation
Reference 49
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 1843b53a-8cc1-4f49-a9de-88f5af30bfe3 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation On the mean-field limit of the Cucker–Smale model with random batch method.Kinetic and Related Models, 18(6):872–910, 2025
Reference 50
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 168080cf-c9a2-42be-86b2-16b20dd5ffe0 · outbound
Mean field error estimate of the random batch method for vortex blob dynamics for the 2D Navier--Stokes Equation 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 51
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.
No inbound Pith citation observations are available.