2011/05/10 by Jacob van den Berg, Berg, Jacob van den, Demeter Kiss +3
Mathematics · Physics and Astronomy · #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR
paper · pdf · doi:10.48550/arxiv.1105.1977
11 pages
arxiv created 2011/05/10 · openalex publication_date 2011/05/10 · arxiv updated 2011/05/11 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We study a percolation process on the planted binary tree, where clusters freeze as soon as they become larger than some fixed parameter N. We show that as N goes to infinity, the process converges in some sense to the frozen percolation process introduced by Aldous. In particular, our results show that the asymptotic behaviour differs substantially from that on the square lattice, on which a similar process has been studied recently by van den Berg, de Lima and Nolin.