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On the Mean-Field Limit for the Vlasov–Poisson–Fokker–Planck System

Publication ,  Journal Article
Huang, H; Liu, JG; Pickl, P
Published in: Journal of Statistical Physics
December 1, 2020

We rigorously justify the mean-field limit of an N-particle system subject to Brownian motions and interacting through the Newtonian potential in R3. Our result leads to a derivation of the Vlasov–Poisson–Fokker–Planck (VPFP) equations from the regularized microscopic N-particle system. More precisely, we show that the maximal distance between the exact microscopic trajectories and the mean-field trajectories is bounded by N-13+ε (163≤ε<136) with a blob size of N-δ (13≤δ<1954-2ε3) up to a probability of 1 - N-α for any α> 0. Moreover, we prove the convergence rate between the empirical measure associated to the regularized particle system and the solution of the VPFP equations. The technical novelty of this paper is that our estimates rely on the randomness coming from the initial data and from the Brownian motions.

Duke Scholars

Published In

Journal of Statistical Physics

DOI

EISSN

1572-9613

ISSN

0022-4715

Publication Date

December 1, 2020

Volume

181

Issue

5

Start / End Page

1915 / 1965

Related Subject Headings

  • Fluids & Plasmas
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Huang, H., Liu, J. G., & Pickl, P. (2020). On the Mean-Field Limit for the Vlasov–Poisson–Fokker–Planck System. Journal of Statistical Physics, 181(5), 1915–1965. https://doi.org/10.1007/s10955-020-02648-3
Huang, H., J. G. Liu, and P. Pickl. “On the Mean-Field Limit for the Vlasov–Poisson–Fokker–Planck System.” Journal of Statistical Physics 181, no. 5 (December 1, 2020): 1915–65. https://doi.org/10.1007/s10955-020-02648-3.
Huang H, Liu JG, Pickl P. On the Mean-Field Limit for the Vlasov–Poisson–Fokker–Planck System. Journal of Statistical Physics. 2020 Dec 1;181(5):1915–65.
Huang, H., et al. “On the Mean-Field Limit for the Vlasov–Poisson–Fokker–Planck System.” Journal of Statistical Physics, vol. 181, no. 5, Dec. 2020, pp. 1915–65. Scopus, doi:10.1007/s10955-020-02648-3.
Huang H, Liu JG, Pickl P. On the Mean-Field Limit for the Vlasov–Poisson–Fokker–Planck System. Journal of Statistical Physics. 2020 Dec 1;181(5):1915–1965.
Journal cover image

Published In

Journal of Statistical Physics

DOI

EISSN

1572-9613

ISSN

0022-4715

Publication Date

December 1, 2020

Volume

181

Issue

5

Start / End Page

1915 / 1965

Related Subject Headings

  • Fluids & Plasmas
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 02 Physical Sciences
  • 01 Mathematical Sciences