7 papers · 1 filter
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…
Sums along the edges of bounded degree graphs
Noga Alon, Itai Benjamini, Georgii Zakharov +1
Let be a graph on vertices and be an abelian group. What is the minimum size of the set of all sums over all injections ? In…
A very sharp threshold for first order logic distinguishability of random graphs
Itai Benjamini, Maksim Zhukovskii
In this paper we find an integer such that the minimum number of variables of a first order sentence that distinguishes between two independent uniformly distributed rando…
Majority dynamics on finite trees
Itai Benjamini, Georgii Zakharov, Maksim Zhukovskii
For an arbitrary finite tree , we find the exact value of the wort-case stabilisation time of majority dynamics on . We also prove that for a perfect rooted cubic tree wi…
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…