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math.PR2025
Random burning of the Euclidean torus
Guillaume Blanc, Alice Contat
The burning number of a graph is the minimal number of steps that are needed to burn all of its vertices, with the following burning procedure: at each step, one can choose a point…
math.PR2023
Percolation with invariant Poisson processes of lines in the -regular tree
Guillaume Blanc
In this paper, we study invariant Poisson processes of lines (i.e, bi-infinite geodesics) in the -regular tree. More precisely, there exists a unique (up to multiplicative const…