9 papers
The critical curve of long-range percolation on oriented trees
Olivier Couronné, Sandro Gallo, Leonardo T. Rolla
We consider a long-range percolation model on homogeneous oriented trees with several lengths. We obtain the critical surface as the set of zeros of a specific polynomial with coef…
An Improved Lower Bound for the Critical Parameter of the Stavskaya's Process via a Generalized Recurrent Method
Olivier Couronné
Stavskaya's process, a discrete-time version of the contact process on , is known to exhibit a phase transition at a critical parameter $\alpc$ whose exact value remains an ope…
An update on lower bounds for the critical values of oriented percolation models
Olivier Couronné
We obtain new lower bounds on the critical points for various models of oriented percolation. The method is to provide a stochastic domination of the percolation processes by multi…
Characterization of the threshold for multi-range percolation on oriented trees
Olivier Couronné
We give a characterization of the percolation threshold for a multirange model on oriented trees, as the first positive root of a polynomial, with the use of a multi-type Galton-Wa…
New upper bound for the connective constant for square-lattice self-avoiding walks
Olivier Couronné
By modifying the automaton used by P{ö}nitz and Tittman [4], and considering loops of length up to 26, we obtain 2.662343 as an upper bound for the connective constant in the latti…
Entanglement percolation and spheres in
Olivier Couronné
We obtain a new lower bound of 0.06576 for the 1-entanglement critical probability (in dimension 3), and prove that the critical point for the existence of a sphere surrounding the…
A Branching-selection process related to censored Galton-Walton processes
Olivier Couronné, Lucas Gerin
We obtain the asymptotics for the speed of a particular case of a particle system with branching and selection introduced by Bérard and Gouéré (2010). The proof is based on a conne…
Construction of a short path in high dimensional First Passage Percolation
Olivier Couronné, Nathanaël Enriquez, Lucas Gerin
For First Passage Percolation in Z^d with large d, we construct a path connecting the origin to {x_1 =1}, whose passage time has optimal order \log d/d. Besides, an improved lower…
Poisson approximation for large clusters in the supercritical FK model
Olivier Couronné
Using the Chen-Stein method, we show that the spatial distribution of large finite clusters in the supercritical FK model approximates a Poisson process when the ratio weak mixing…