149 citations · 189 across the 19 of their papers we have counts for
22 papers
Uniform-in-time relative entropy estimates for Kac's approximation of the Landau equation
Xuanrui Feng, Chenguang Liu, Zhenfu Wang
We prove uniform-in-time quantitative relative entropy estimates for Kac's particle approximation of the three-dimensional spatially homogeneous Landau equation for Maxwellian mole…
Purified Projection Method and Uhlmann Fidelity for Mixed Hartree Dynamics
Hao Liang, Zhenfu Wang
We give a purification and fidelity formulation of the projection method for mixed Hartree data. For the mean-field evolution of -particle density matrices, we prove quantitativ…
Quantum Relative Entropy and the Mean-Field Limit
Gaoyue Guo, Hao Liang, Zhenfu Wang
We develop a quantum relative entropy method for the mean-field limit of quantum many-body systems. For closed systems governed by the von Neumann equation, we prove a quantitative…
Kac's Program for the Landau Equation
Xuanrui Feng, Zhenfu Wang
We study the derivation of the spatially homogeneous Landau equation from the mean-field limit of a conservative -particle system, obtained by passing to the grazing limit on Ka…
Propagation of Chaos for 2D Log Gas on the Whole Space
Shuzhe Cai, Xuanrui Feng, Yun Gong +1
We derive the quantitative propagation of chaos in the sense of relative entropy for the first time for the 2D Log gas or the weakly interacting particle systems with 2D Coulomb in…
Quantitative Propagation of Chaos for 2D Viscous Vortex Model with General Circulations on the Whole Space
Xuanrui Feng, Zhenfu Wang
We derive quantitative propagation of chaos in the sense of relative entropy for the 2D viscous vortex model with general circulations, approximating the vorticity formulation of t…
Relative Entropy Method for Particle Approximation of the Landau Equation for Maxwellian Molecules
José Antonio Carrillo, Xuanrui Feng, Shuchen Guo +2
We derive the spatially homogeneous Landau equation for Maxwellian molecules from a natural stochastic interacting particle system. More precisely, we control the relative entropy…
Uniform-in-time propagation of chaos for second order interacting particle systems
Yun Gong, Zhenfu Wang, Pengzhi Xie
We study the long time behavior of second order particle systems interacting through global Lipschitz kernels. Combining hypocoercivity method in [37] and relative entropy method i…
Transport based particle methods for the Fokker-Planck-Landau equation
Vasily Ilin, Jingwei Hu, Zhenfu Wang
We propose a particle method for numerically solving the Landau equation, inspired by the score-based transport modeling (SBTM) method for the Fokker-Planck equation. This method c…
Quantitative Propagation of Chaos for 2D Viscous Vortex Model on the Whole Space
Xuanrui Feng, Zhenfu Wang
We derive the quantitative estimates of propagation of chaos for the large interacting particle systems in terms of the relative entropy between the joint law of the particles and…
Entropy-dissipation Informed Neural Network for McKean-Vlasov Type PDEs
Zebang Shen, Zhenfu Wang
We extend the concept of self-consistency for the Fokker-Planck equation (FPE) to the more general McKean-Vlasov equation (MVE). While FPE describes the macroscopic behavior of par…
Mean-field limit of Non-exchangeable interacting diffusions with singular kernels
Zhenfu Wang, Xianliang Zhao, Rongchan Zhu
The mean-field limit of interacting diffusions without exchangeability, caused by weighted interactions and non-i.i.d. initial values, are investigated. The weights could be signed…
Self-Consistency of the Fokker-Planck Equation
Zebang Shen, Zhenfu Wang, Satyen Kale +3
The Fokker-Planck equation (FPE) is the partial differential equation that governs the density evolution of the Itô process and is of great importance to the literature of statisti…
Gaussian fluctuations for interacting particle systems with singular kernels
Zhenfu Wang, Xianliang Zhao, Rongchan Zhu
We consider the asymptotic behavior of the fluctuations for the empirical measures of interacting particle systems with singular kernels. We prove that the sequence of fluctuation…
Mean-field limit and quantitative estimates with singular attractive kernels
Didier Bresch, Pierre-Emmanuel Jabin, Zhenfu Wang
This paper proves the mean field limit and quantitative estimates for many-particle systems with singular attractive interactions between particles. As an important example, a full…
Sinkhorn Natural Gradient for Generative Models
Zebang Shen, Zhenfu Wang, Alejandro Ribeiro +1
We consider the problem of minimizing a functional over a parametric family of probability measures, where the parameterization is characterized via a push-forward structure. An im…
Sinkhorn Barycenter via Functional Gradient Descent
Zebang Shen, Zhenfu Wang, Alejandro Ribeiro +1
In this paper, we consider the problem of computing the barycenter of a set of probability distributions under the Sinkhorn divergence. This problem has recently found applications…
Modulated Free Energy and Mean Field Limit
Didier Bresch, Pierre-Emmanuel Jabin, Zhenfu Wang
This is the document corresponding to the talk the first author gave at IH{É}S for the Laurent Schwartz seminar on November 19, 2019. It concerns our recent introduction of a modul…
On Mean Field Limit and Quantitative Estimates with a Large Class of Singular Kernels: Application to the Patlak-Keller-Segel Model
Didier Bresch, Pierre-Emmanuel Jabin, Zhenfu Wang
In this note, we propose a new relative entropy combination of the methods developed by P.--E. Jabin and Z.~Wang [Inventiones (2018)] and by S. Serfaty [Proc. Int. Cong. of Math, (…
Uniqueness of Bounded Solutions for the Homogeneous Relativistic Landau Equation with Coulomb Interactions
Robert M. Strain, Zhenfu Wang
We prove the uniqueness of weak solutions to the spatially homogeneous special relativistic Landau equation under the conditional assumption that the solution satisfies $(p^0)^7 F(…
Quantitative estimate of propagation of chaos for stochastic systems with kernels
Pierre-Emmanuel Jabin, Zhenfu Wang
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 t…
Mean Field Limit and Propagation of Chaos for Vlasov Systems with Bounded Forces
Pierre-Emmanuel Jabin, Zhenfu Wang
We consider large systems of particles interacting through rough but bounded interaction kernels. We are able to control the relative entropy between the -particle distribution…