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A note on percolation on $Z^d$: isoperimetric profile via exponential cluster repulsion
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 isExpand
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  • 6
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 randomExpand
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  • 6
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 withExpand
  • 25
  • 5
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 ruleExpand
  • 90
  • 4
On the entropy of the sum and of the difference of independent random variables
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 forExpand
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Random disease on the square grid
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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 incidentExpand
  • 17
  • 2
Critical percolation on certain nonunimodular graphs
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
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  • 2
And the Square Root of 17
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 incidentExpand
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