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math.PR2024
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…
math.PR2024
On the intersection of critical percolation clusters and other tree-like random graphs
Amine Asselah, Bruno Schapira
We study intersection properties of two or more independent tree-like random graphs. Our setting encompasses critical, possibly long range, Bernoulli percolation clusters, incipien…