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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…
Universality for catalytic equations and fully parked trees
Alice Contat, Nicolas Curien
We show that critical parking trees conditioned to be fully parked converge in the scaling limits towards the Brownian growth-fragmentation tree, a self-similar Markov tree differe…
Blow-up rate of solution to generalised Blasius equation
Guillaume Blanc, Alice Contat
We identify the blow-up rate of a solution to a generalised Blasius equation, that we came across while studying a probabilistic model of "Poissonian burning" in Euclidean space. O…
Parking on the Random Recursive Tree
Alice Contat, Lucile Laulin
We study the parking process on the random recursive tree. We first prove that although the random recursive tree has a non-degenerate Benjamini--Schramm limit, the phase transitio…