A note on the rightmost particle in a Fleming-Viot process

TL;DR

This paper analyzes a Fleming-Viot particle system with N nearest neighbor random walks drifting towards zero, demonstrating ergodicity and providing exponential moment bounds for the rightmost particle under the stationary distribution.

Contribution

It establishes ergodicity and exponential moment bounds for the rightmost particle in a Fleming-Viot process with nearest neighbor random walks.

Findings

The particle system is ergodic.

Exponential moments of the rightmost position are established.

Results hold under the stationary measure.

Abstract

We consider N nearest neighbor random walks on the positive integers with a drift towards the origin. When one walk reaches the origin, it jumps to the position of one of the other N-1 walks, chosen uniformly at random. We show that this particle system is ergodic, and establish some exponential moments of the rightmost position, under the stationary measure.