10 papers
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…
On the first and second largest components in the percolated Random Geometric Graph
Lyuben Lichev, Bas Lodewijks, Dieter Mitsche +1
The percolated random geometric graph has vertex set given by a Poisson Point Process in the square , and every pair of vertices at distance at most 1…