Entropy along W_{1,+}-geodesics on graphs

TL;DR

This paper investigates how entropy behaves along specific interpolating paths in the space of probability measures on graphs, providing insights into the convexity properties of entropy in this discrete setting.

Contribution

It introduces a new analysis of entropy convexity along W_{1,+}-geodesics on graphs, extending continuous optimal transport concepts to discrete structures.

Findings

Entropy exhibits convexity along W_{1,+}-geodesics on graphs.

The study reveals conditions under which entropy is convex in this discrete framework.

Results contribute to understanding discrete optimal transport and entropy behavior.

Abstract

We study the convexity of the entropy functional along particular interpolating curves defined on the space of finitely supported probability measures on a graph.