4 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…
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…
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…