Lazy random walks and optimal transport on graphs

DOI10.1214/15-AOP1012zbMath1397.60109arXiv1308.0226OpenAlexW2964328909MaRDI QIDQ726796

Christian Léonard

Publication date: 14 July 2016

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.0226

zbMATH Keywords

random walks\(\Gamma\)-convergenceoptimal transportSchrödinger problementropy minimizationdiscrete metric graphdisplacement interpolation

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Numerical optimization and variational techniques (65K10) Variational problems in a geometric measure-theoretic setting (49Q20) Methods involving semicontinuity and convergence; relaxation (49J45) Continuous-time Markov processes on discrete state spaces (60J27)

Related Items (14)

Some recent developments in functional inequalities ⋮ LAZY RANDOM WALKS ON PSEUDOFRACTAL SCALE-FREE WEB WITH A PERFECT TRAP ⋮ Vector-Valued Optimal Mass Transport ⋮ Nonexponential Sanov and Schilder theorems on Wiener space: BSDEs, Schrödinger problems and control ⋮ Dynamical Schrödinger bridge problems on graphs ⋮ A survey of the Schrödinger problem and some of its connections with optimal transport ⋮ The Most Likely Evolution of Diffusing and Vanishing Particles: Schrödinger Bridges with Unbalanced Marginals ⋮ A second order equation for Schrödinger bridges with applications to the hot gas experiment and entropic transportation cost ⋮ Absolutely continuous and BV-curves in 1-Wasserstein spaces ⋮ Entropic Ricci Curvature for Discrete Spaces ⋮ What is a stochastic Hamiltonian process on finite graph? An optimal transport answer ⋮ The Markov-quantile process attached to a family of marginals ⋮ Stochastic Control Liaisons: Richard Sinkhorn Meets Gaspard Monge on a Schrödinger Bridge ⋮ Entropic curvature on graphs along Schrödinger bridges at zero temperature

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