Showing math.PRShow all
3 papers · 1 filter
math.PR2025
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…
math.PR2025
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…
math.PR2007
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…