Discrete Ricci curvature bounds for Bernoulli-Laplace and random transposition models

TL;DR

This paper computes Ricci curvature bounds for specific classical random walk models, including the Bernoulli-Laplace model and the random transposition shuffle, providing insights into their geometric properties.

Contribution

It introduces explicit Ricci curvature bounds for these well-known random walk models, advancing the understanding of their geometric and probabilistic structure.

Findings

Ricci curvature bounds for Bernoulli-Laplace model

Ricci curvature bounds for random transposition shuffle

Enhanced understanding of geometric properties of these models

Abstract

We calculate a Ricci curvature lower bound for some classical examples of random walks, namely, a chain on a slice of the n-dimensional discrete cube (the so-called Bernoulli-Laplace model) and the random transposition shuffle of the symmetric group of permutations on n letters.