## View abstract

### Session S06 - Interacting Stochastic Systems

Tuesday, July 13, 15:25 ~ 16:00 UTC-3

## Mean Field behavior in Coalescing Random Walk

### Jonathan Hermon

#### University of British Columbia, Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak6ee295defdaa19932972c62bec192d83').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy6ee295defdaa19932972c62bec192d83 = 'jh&#101;rm&#111;n' + '&#64;'; addy6ee295defdaa19932972c62bec192d83 = addy6ee295defdaa19932972c62bec192d83 + 'm&#97;th' + '&#46;' + '&#117;bc' + '&#46;' + 'c&#97;'; var addy_text6ee295defdaa19932972c62bec192d83 = 'jh&#101;rm&#111;n' + '&#64;' + 'm&#97;th' + '&#46;' + '&#117;bc' + '&#46;' + 'c&#97;';document.getElementById('cloak6ee295defdaa19932972c62bec192d83').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy6ee295defdaa19932972c62bec192d83 + '\'>'+addy_text6ee295defdaa19932972c62bec192d83+'<\/a>';

We study Coalescing Random Walks on general graphs. We determine the asymptotic of the probability that the origin is occupied at time t for transient vertex-transitive graphs. Previously this probability was only known for $\mathbb{Z}^d$. We prove analogous results for finite graphs (vertex transitive or the configuration model with minimal degree 3) under certain finitary notions of transience. In particular, it follows that the number of remaining particles evolves like Kingman's coalescence up to a scaling of the time by a constant with a certain probabilistic interpretation.

Joint work with Shuangping Li,, Dong Yao, and Lingfu Zhang.