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Pivotal, cluster, and interface measures for critical planar percolation

- C. Garban, G. Pete, O. Schramm
- Mathematics
- 8 August 2010

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… Expand

The Fourier spectrum of critical percolation

- C. Garban, G. Pete, O. Schramm
- Mathematics
- 26 March 2008

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… Expand

Scale-invariant groups

- V. Nekrashevych, G. Pete
- Mathematics
- 3 November 2008

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… Expand

Bootstrap Percolation on Infinite Trees and Non-Amenable Groups

TLDR

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

- Dayue Chen, Y. Peres, G. Pete
- Mathematics
- 26 March 2003

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

TLDR

The scaling limits of near-critical and dynamical percolation

- C. Garban, G. Pete, O. Schramm
- Mathematics
- 23 May 2013

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 $\mathcal{H}$… Expand

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

- A. Lapidoth, G. Pete
- Computer Science, MathematicsIEEE 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
- 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

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