Skip to content
DraconiticResearch
Search Sources API
201,683 studies31 sourcesUpdated 22 min ago
PreprintCC BY 4.0arXiv

On the diffusive-mean field limit of a kinetic weakly interacting particle system

  • Raphaël Gastaldello
  • Grigorios A. Pavliotis
  • Gabriel Stoltz
  • Urbain Vaes
Open at sourcePDFDOICite

Abstract

We study the joint diffusive-mean field limit for a system of weakly interacting kinetic Langevin dynamics, extending the results of Delgadino, Gvalani and Pavliotis (Arch. Ration. Mech. Anal., 2021) to the hypoelliptic/hypocoercive case. We show that, in the absence of phase transitions, the two limits commute, and we calculate the covariance matrix of the limiting Brownian motion using the Green-Kubo/Kipnis-Varadhan formula. However, at low temperatures, and in the presence of phase transitions, the two limits may not commute. We demonstrate our findings by providing a detailed analysis of the diffusive-mean field limit for the O(2) model in a magnetic field. Our analysis is based on the systematic use of recently developed hypocoercivity techniques, together with an appropriate linearization of the mean field McKean-Vlasov-Fokker-Planck partial differential equation.

Related

  1. On the asymptotic behavior at the kinetic time of a weakly interacting Fermi gas
    Peter S. Madsen, Phan Thành Nam, Herbert Spohn +1
    arXivPreprintarXiv licenceFull textMathematical physicsarXiv
  2. Tamed Euler Approximation of Invariant Measures for Weakly Interacting Particle Systems and McKean--Vlasov Equations
    Lingyan Cheng, Ruinan Li, Shiyu Liu +1
    arXivPreprintCC BY-NC-ND 4.0Full textProbabilityarXiv
  3. Kinetic interacting particle Langevin Monte Carlo
    Paul Valsecchi Oliva, Ömer Deniz Akyıldız
    Statistics and ComputingPeer-reviewedCC BYFull text12 citedStatisticsOpenAlex
  4. Ensemble Kalman Inversion as an Inertial Interacting Particle System
    Michael Herty, Pierpaolo Porretta, Giuseppe Visconti
    arXivPreprintarXiv licenceFull textDynamical systemsNumerical analysis & scientific computingarXiv
  5. Kinetic Wedge Layers and Diffusive Limit of Neutron Transport in Polygonal Domains
    Zhimeng Ouyang, Lei Wu
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{gastaldello2026diffusivemean,
  title = {{On the diffusive-mean field limit of a kinetic weakly interacting particle system}},
  author = {Raphaël Gastaldello and Grigorios A. Pavliotis and Gabriel Stoltz and Urbain Vaes},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2607.15896},
  eprint = {2607.15896},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.15896},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the diffusive-mean field limit of a kinetic weakly interacting particle system
AU  - Raphaël Gastaldello
AU  - Grigorios A. Pavliotis
AU  - Gabriel Stoltz
AU  - Urbain Vaes
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2607.15896
UR  - https://arxiv.org/abs/2607.15896
AB  - We study the joint diffusive-mean field limit for a system of weakly interacting kinetic Langevin dynamics, extending the results of Delgadino, Gvalani and Pavliotis (Arch. Ration. Mech. Anal., 2021) to the hypoelliptic/hypocoercive case. We show that, in the absence of phase transitions, the two limits commute, and we calculate the covariance matrix of the limiting Brownian motion using the Green-Kubo/Kipnis-Varadhan formula. However, at low temperatures, and in the presence of phase transitions, the two limits may not commute. We demonstrate our findings by providing a detailed analysis of the diffusive-mean field limit for the O(2) model in a magnetic field. Our analysis is based on the systematic use of recently developed hypocoercivity techniques, together with an appropriate linearization of the mean field McKean-Vlasov-Fokker-Planck partial differential equation.
ER  -