39 citations · 96 across the 20 of their papers we have counts for
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Probabilistic proof for non-survival at criticality : the Galton-Watson process and more
Olivier Garet
In a famous paper, Bezuidenhout and Grimmett demonstrated that the contact process dies out at the critical point.Their proof technique has often been used to study the growth of p…
A central limit theorem for the number of descents and some urn models
Olivier Garet
The purpose of this work is to establish a central limit theorem that can be applied to a particular form of Markov chains, including the number of descents in a random permutation…
Percolation and first-passage percolation on oriented graphs
Olivier Garet, Régine Marchand
We give the first properties of independent Bernoulli percolation, for oriented graphs on the set of vertices that are translation-invariant and may contain loops. We exhibi…
Does Eulerian percolation on percolate ?
Olivier Garet, Regine Marchand, Irène Marcovici
Eulerian percolation on Z 2 with parameter p is the classical Bernoulli bond percolation with parameter p conditioned on the fact that every site has an even degree. We first expla…
Continuity of the time and isoperimetric constants in supercritical percolation
Olivier Garet, Régine Marchand, Eviatar B. Procaccia +1
We consider two different objects on super-critical Bernoulli percolation on : the time constant for i.i.d. first-passage percolation (for ) and the isoperi…
Continuity of the asymptotic shape of the supercritical contact process
Olivier Garet, Régine Marchand, Marie Théret
We prove the continuity of the shape governing the asymptotic growth of the supercritical contact process in Z^d , with respect to the infection parameter. The proof is valid in an…