# Spectral Gap for Measure-Valued Diffusion Processes

## TL;DR

This paper estimates the spectral gap for measure-valued diffusion processes on Riemannian manifolds, providing explicit convergence rates to distributions relevant in population genetics.

## Contribution

It introduces explicit spectral gap estimates for measure-valued diffusions, enhancing understanding of their convergence behavior on Riemannian manifolds.

## Key findings

- Explicit spectral gap estimates derived.
- Convergence rates to Dirichlet and Gamma distributions established.
- Applications to population genetics models.

## Abstract

The spectral gap is estimated for measure-valued diffusion processes induced by the intrinsic/extrinsic derivatives on the space of finite measures over a Riemannian manifold. This provides explicit exponential convergence rate for these processes to approximate the Dirichlet and Gamma distributions arising from population genetics.