The scaling limit of the Minimal Spanning Tree - a preliminary report (2009)
Garban, Christophe, Pete, Gábor, Schramm, Oded
This is a short (and somewhat informal) contribution to the proceedings of the XVIth International Congress on Mathematical Physics, Prague, 2009, written up by the second author. We describe how the...
Bootstrap percolation on infinite trees and non-amenable groups (2008)
József Balogh, Yuval Peres, Gábor Pete
Abstract. Bootstrap percolation on an arbitrary graph has a random initial configu-ration, where each vertex is occupied with probability p, independently of each other, and a deterministic spreading...
Biased tug-of-war, the biased infinity Laplacian, and comparison with exponential cones (2008)
Peres, Yuval, Pete, Gábor, Somersille, Stephanie
We prove that if U\subset\R^n is an open domain whose closure \overline{U} is compact in the path metric, and F is a Lipschitz function on \partial{U}, then for each \beta\in\R there exists a unique...
Nekrashevych, Volodymyr, Pete, Gábor
Motivated by the renormalization method in statistical physics, Itai Benjamini defined a finitely generated infinite group G to be scale-invariant if there is a nested sequence of finite index...
1 Introduction Glauber Dynamics on Trees (2008)
Manjunath Krishnapur, Gábor Pete
This paper deals with Glauber dynamics for the Ising model on trees, with [5] as the primary reference. As explained below, Ising model on trees has an interpretation in terms of information
Disease Process and Bootstrap Percolation (2008)
1. Deterministic disease on the k-dimensional board........................... 3
Corner percolation on $\mathbb{Z}^2$ and the square root of 17 (2005)
We consider a four-vertex model introduced by B\'{a}lint T\'{o}th: a dependent bond percolation model on $\mathbb{Z}^2$ in which every edge is present with probability 1/2 and each vertex has exactly...
Anchored expansion, percolation and speed (2004)
Chen, Dayue, Peres, Yuval, Pete, Gábor
Benjamini, Lyons and Schramm [Random Walks and Discrete Potential Theory (1999) 56–84] considered properties of an infinite graph G, and the simple random walk on it, that are preserved by random...
Random disease on the square grid (1998)
Abstract. We introduce some generalizations of a nice combinatorial problem, the central notion of which is the so-called Disease Process. Let us color independently each square of an n×n chessboard...