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Pivotal, cluster, and interface measures for critical planar percolation
This work is the first in a series of papers devoted to the construction and study of scaling limits of dynamical and near-critical planar percolation and related objects like invasion percolation…
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The Fourier spectrum of critical percolation
Consider the indicator function f of a 2-dimensional percolation crossing event. In this paper, the Fourier transform of f is studied and sharp bounds are obtained for its lower tail in several…
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Scale-invariant groups
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…
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Bootstrap Percolation on Infinite Trees and Non-Amenable Groups
TLDR
It is proved that on any $2k-regular non-amenable graph, the critical probability for the $k$-rule is strictly positive, and that in any rooted tree $T$ there is a way of erasing children of the root, together with all their descendants, and repeating this for all remaining children, and so on.
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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 is…
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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…
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Random disease on the square grid
TLDR
The main result of this paper is the almost exact determination of the threshold function in the fundamental case of this Random Disease Problem.
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The scaling limits of near-critical and dynamical percolation
We prove that near-critical percolation and dynamical percolation on the triangular lattice $\eta \mathbb{T}$ have a scaling limit as the mesh $\eta \to 0$, in the "quad-crossing" space $\mathcal{H}$…
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On the entropy of the sum and of the difference of independent random variables
  • A. Lapidoth, G. Pete
  • Computer Science, 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…
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Corner percolation on ℤ2 and the square root of 17
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…
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