30 citations · 69 across the 46 of their papers we have counts for
55 papers · 1 filter
Vertex reinforced branching random walks and generalized time-dependent Polya urns
Bruno Schapira
We consider a class of infinite critical tree-indexed random walks on , where the motion of particles is subject to vertex reinforcement. We mainly focus on the strong r…
On reversing the Simon-Lieb inequality in high-dimensional percolation
Romain Panis, Bruno Schapira
We study Bernoulli percolation on in dimensions . We prove that a classical consequence of the van den Berg-Kesten inequality, often referred to as the Simon-L…
Sharp bounds on the half-space two-point function for high-dimensional Bernoulli percolation
Romain Panis, Bruno Schapira
We consider Bernoulli percolation on with . We prove an up-to-constant estimate for the critical two-point function restricted to a half-space. This completes pr…
Derivative formula for capacities
Amine Asselah, Bruno Schapira, Perla Sousi
We obtain a derivative formula for various notions of capacity. Namely we identify the second order term in the asymptotic expansion of the capacity of a union of two sets, as thei…
Capacity in high dimensional percolation
Amine Asselah, Bruno Schapira, Perla Sousi
We introduce a notion of capacity for high dimensional critical percolation by showing that for any finite set , the suitably rescaled probability that the cluster of inters…
A localisation phase transition for the catalytic branching random walk
Cécile Mailler, Bruno Schapira
We show the existence of a phase transition between a localisation and a non-localisation regime for a branching random walk with a catalyst at the origin. More precisely, we consi…