主 题: Optimal transport and entropy dissipation on finite graphs
报告人: Professor Shui-Nee Chow (Georgia Institute of Technology )
时 间: 2016-10-14 15：00-16：00
地 点: 理科一号楼 1114（数学所活动）
In recent years, optimal transport is essential in geometry and
partial differential equations. We consider a similar setting on
discrete states, which are modeled by finite but arbitrary graphs.
By defining a 2-Wasserstein metric on graphs, we introduce a
dynamical system (a Fokker-Planck equation on graph), which is
a gradient flow of a discrete free energy. We prove that the
gradient flow is dissipative and converges to a discrete Gibbs
measure at an exponential dissipation rate. Our derivation
provides tools for functional inequalities, numerics for nonlinear
partial differential equations and geometry (Yano formula).
This is joint work with my colleagues: Wilfrid Gangbo (UCLA),
Wuchen Li (UCLA) and Haomin Zhou(Georgia Institute of
Technology).
