56 citations · 180 across the 28 of their papers we have counts for
24 papers · 1 filter
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…
Existence of phase transition for percolation using the Gaussian Free Field
Hugo Duminil-Copin, Subhajit Goswami, Aran Raoufi +2
In this paper, we prove that Bernoulli percolation on bounded degree graphs with isoperimetric dimension undergoes a non-trivial phase transition (in the sense that ).…
Upper bounds on the growth rate of Diffusion Limited Aggregation
Itai Benjamini, Ariel Yadin
We revisit Kesten's argument for the upper bound on the growth rate of DLA. We are able to make the argument robust enough so that it applies to many graphs, where only control of…
Minimal growth harmonic functions on lamplighter groups
Itai Benjamini, Hugo Duminil-Copin, Gady Kozma +1
We study the minimal possible growth of harmonic functions on lamplighters. We find that has no sublinear harmonic functions, $(\mathbb{Z}/2)\wr \mat…
Indicable groups and
Aran Raoufi, Ariel Yadin
A conjecture of Benjamini & Schramm from 1996 states that any finitely generated group that is not a finite extension of Z has a non-trivial percolation phase. Our main results pro…
Self-avoiding walks on finite graphs of large girth
Ariel Yadin
We consider self-avoiding walk on finite graphs with large girth. We study a few aspects of the model originally considered by Lawler, Schramm and Werner on finite balls in Z^d. Th…