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- Publications
- Influence

A note on percolation on $Z^d$: isoperimetric profile via exponential cluster repulsion

- G. Pete
- Mathematics
- 16 February 2007

We show that for all $p>p_c(\mathbb{Z}^d)$ percolation parameters, the probability that the cluster of the origin is finite but has at least $t$ vertices at distance one from the infinite cluster is… Expand

Anchored expansion, percolation and speed

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… Expand

Random disease on the square grid

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 black with… Expand

Bootstrap Percolation on Infinite Trees and Non-Amenable Groups

Bootstrap percolation on an arbitrary graph has a random initial configuration, where each vertex is occupied with probability $p$, independently of each other, and a deterministic spreading rule… Expand

On the entropy of the sum and of the difference of independent random variables

- A. Lapidoth, G. Pete
- Mathematics
- IEEE 25th Convention of Electrical and…
- 1 March 2008

We show that the entropy of the sum of independent random variables can greatly differ from the entropy of their difference. The gap between the two entropies can be arbitrarily large. This holds for… Expand

Corner percolation on ℤ2 and the square root of 17

- G. Pete
- Physics, Mathematics
- 22 July 2005

We consider a four-vertex model introduced by Balint Toth: a dependent bond percolation model on Ζ 2 in which every edge is present with probability 1/2 and each vertex has exactly two incident… Expand

Critical percolation on certain nonunimodular graphs

- Y. Peres, G. Pete, A. Scolnicov
- Mathematics
- 29 January 2005

An important conjecture in percolation theory is that almost sure- ly no infinite cluster exists in critical percolation on any transitive graph for which the critical probability is less than 1.… Expand

And the Square Root of 17

- Gábor Pete
- 2005

We consider a four-vertex model introduced by Bálint Tóth: a dependent bond percolation model on Z, in which every edge is present with probability 1/2, and each vertex has exactly two incident… Expand

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