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

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.

9 pages

References in corpus (5)

• Convergence in law of the minimum of a branching random walk
• Configurational transition in a Fleming-Viot-type model and probabilistic interpretation of Laplacian eigenfunctions
• The branching Brownian motion seen from its tip
• The Extremal Process of Branching Brownian Motion
• Branching Brownian motion with selection of the N right-most particles: An approximate model

Cited by in corpus (2)

• A non-conservative Harris ergodic theorem
• Dynamics of a Fleming-Viot type particle system on the cycle graph