5 papers · 1 filter
Random burning of the Euclidean lattice
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…
The critical Karp--Sipser core of random graphs
Thomas Budzinski, Alice Contat, Nicolas Curien
We study the Karp--Sipser core of a random graph made of a configuration model with vertices of degree and . This core is obtained by recursively removing the leaves as we…
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…
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…
The critical Karp--Sipser core of ErdÅs--Rényi random graphs
Thomas Budzinski, Alice Contat
The Karp--Sipser algorithm consists in removing recursively the leaves as well their unique neighbours and all isolated vertices of a given graph. The remaining graph obtained when…