Propagation of chaos: a review of models, methods and applications. I. Models and methods
LP Chaintron, A Diez - arXiv preprint arXiv:2203.00446, 2022 - arxiv.org
The notion of propagation of chaos for large systems of interacting particles originates in
statistical physics and has recently become a central notion in many areas of applied …
statistical physics and has recently become a central notion in many areas of applied …
Propagation of chaos: a review of models, methods and applications. II. Applications
LP Chaintron, A Diez - arXiv preprint arXiv:2106.14812, 2021 - arxiv.org
The notion of propagation of chaos for large systems of interacting particles originates in
statistical physics and has recently become a central notion in many areas of applied …
statistical physics and has recently become a central notion in many areas of applied …
[图书][B] Topics in optimal transportation
C Villani - 2021 - books.google.com
This is the first comprehensive introduction to the theory of mass transportation with its many—
and sometimes unexpected—applications. In a novel approach to the subject, the book both …
and sometimes unexpected—applications. In a novel approach to the subject, the book both …
[图书][B] Optimal transport: old and new
C Villani - 2009 - Springer
At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and
John Mather launched a revolution in the venerable field of optimal transport founded by G …
John Mather launched a revolution in the venerable field of optimal transport founded by G …
A review of mathematical topics in collisional kinetic theory
C Villani - Handbook of mathematical fluid dynamics, 2002 - books.google.com
The goal of this review paper is to provide the reader with a concise introduction to the
mathematical theory of collision processes in (dilute) gases and plasmas, viewed as a …
mathematical theory of collision processes in (dilute) gases and plasmas, viewed as a …
Quantitative estimates of propagation of chaos for stochastic systems with kernels
PE Jabin, Z Wang - Inventiones mathematicae, 2018 - Springer
We derive quantitative estimates proving the propagation of chaos for large stochastic
systems of interacting particles. We obtain explicit bounds on the relative entropy between …
systems of interacting particles. We obtain explicit bounds on the relative entropy between …
Hierarchies, entropy, and quantitative propagation of chaos for mean field diffusions
D Lacker - Probability and Mathematical Physics, 2023 - msp.org
This paper develops a nonasymptotic, local approach to quantitative propagation of chaos
for a wide class of mean field diffusive dynamics. For a system of n interacting particles, the …
for a wide class of mean field diffusive dynamics. For a system of n interacting particles, the …
Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
JA Carrillo, RJ McCann, C Villani - Revista Matematica Iberoamericana, 2003 - ems.press
The long-time asymptotics of certain nonlinear, nonlocal, diffusive equations with a gradient
flow structure are analyzed. In particular, a result of Benedetto, Caglioti, Carrillo and …
flow structure are analyzed. In particular, a result of Benedetto, Caglioti, Carrillo and …
Sharp uniform-in-time propagation of chaos
We prove the optimal rate of quantitative propagation of chaos, uniformly in time, for
interacting diffusions. Our main examples are interactions governed by convex potentials …
interacting diffusions. Our main examples are interactions governed by convex potentials …
Mean field limit for stochastic particle systems
PE Jabin, Z Wang - Active Particles, Volume 1: Advances in Theory …, 2017 - Springer
We review some classical and more recent results for the derivation of mean field equations
from systems of many particles, focusing on the stochastic case where a large system of …
from systems of many particles, focusing on the stochastic case where a large system of …