Cutoff in separation for compact harmonic manifold

TL;DR

This paper demonstrates the occurrence of cutoff in separation for Brownian motion on specific compact harmonic manifolds, providing explicit cutoff times and windows for these families.

Contribution

It establishes the presence of cutoff phenomena in Brownian motion on certain compact harmonic manifolds and computes precise cutoff parameters.

Findings

Cutoff occurs in separation for Brownian motion on S^n, CP^n, HP^n, RP^n.

Explicit cutoff times and windows are computed for these manifolds.

The proof uses sharp strong stationary times and asymptotic expansions.

Abstract

We show that cutoff in separation occurs for Brownian motion in some families of compact harmonic manifolds. We compute the cutoff time and windows in four families of compact harmonic manifold namely S n , CP n , HP n and RP n (the first three families are the only families of compact simply connected harmonic manifolds, see [19]). The proof is based on sharp strong stationary times and sufficiently accurate asymptotic expansions of their means and variances.