7 papers · 1 filter
The Conclave Process
Itai Benjamini, Zhenhao Cai, Guanyi Chen +2
We introduce a stochastic model for the papal conclave in which cardinals vote repeatedly among themselves until one cardinal receives all the votes. In each round, the probabi…
How fast does the range of simple random walk grow?
Itai Benjamini, Justin Salez
Consider a discrete-time simple random walk on an infinite, connected, locally finite simple graph , and let \[ R_t := |\{X_0,\ldots,X_t\}| \] denote its range.…
The Pile Process on a Cycle
Itai Benjamini, Eric Shellef
Consider a finite particle system in which, at each step, one particle from a vertex with a lower neighboring vertex moves to a neighboring vertex of minimum height. For the cycle…
First Passage percolation on a hyperbolic graph admits bi-infinite geodesics
Itai Benjamini, Romain Tessera
Given an infinite connected graph, a way to randomly perturb its metric is to assign random i.i.d. lengths to the edges. An open question attributed to Furstenberg is whether there…
Phase transition for recurrence of stationary random walks on lamplighter groups
Itai Benjamini, Guy Blachar, Ariel Yadin
We introduce and study a class of random walks on lamplighter groups , where is a nontrivial finitely generated group and is an infinite finitely generated group, c…
On an epidemic model on finite graphs
Itai Benjamini, Luiz Renato Fontes, Jonathan Hermon +1
We study a system of random walks, known as the frog model, starting from a profile of independent Poisson() particles per site, with one additional active particle planted at…