Semi-classical analysis of a random walk on a manifold

TL;DR

This paper establishes a precise rate at which a natural random walk on a compact Riemannian manifold converges to its stationary distribution, supported by spectral analysis of the related operator.

Contribution

It provides a sharp convergence rate for a random walk on manifolds and offers a detailed spectral theory analysis of the associated operator.

Findings

Proves a sharp convergence rate to stationarity.

Analyzes spectral properties of the operator.

Connects geometric structure with probabilistic behavior.

Abstract

We prove a sharp rate of convergence to stationarity for a natural random walk on a compact Riemannian manifold $(M,g)$. The proof includes a detailed study of the spectral theory of the associated operator.