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

Amine Asselah (1) , Marie-Noémie Thai

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Domaines: Probabilités [math.PR]

Amine Asselah, Marie-Noémie Thai. A note on the rightmost particle in a Fleming-Viot process. 2012. ⟨hal-00795842⟩