Separation and coupling cutoffs for tuples of independent Markov processes

TL;DR

This paper investigates the conditions under which a collection of independent ergodic Markov processes exhibits a separation cutoff, providing criteria, bounds, and connections to extreme value theory.

Contribution

It establishes a necessary and sufficient condition for the separation cutoff in n-tuples of independent Markov processes and links cutoff phenomena to extreme value theory.

Findings

Characterization of separation cutoff conditions

Bounds on cutoff window size

Connections to extreme value theory

Abstract

We consider an $n$-tuple of independent ergodic Markov processes, each of which converges (in the sense of separation distance) at an exponential rate, and obtain a necessary and sufficient condition for the $n$-tuple to exhibit a separation cutoff. We also provide general bounds on the (asymmetric) window size of the cutoff, and indicate links to classical extreme value theory.