Seminário em Probabilidade e Processos Estocásticos Projeto FAPESP - Modelagem estocástica de sistemas interagentes - Frozen Percolation
Bernardo N. B. de Lima (Departamento de Matemática - UFMG)
12 de abril de 2012

Frozen Percolation was introduced by D. Aldous in 2000, and is defined as follows. Consider a family of i.i.d. random variables indexed by the vertices of a graph, (U_v), with uniform distribution in [0,1]. At time t=0 all sites are inactive, and site v becomes active at time U_v. When an infinite cluster of active sites appears, all sites of this cluster become frozen. Then, at time t=1 all sites are active or frozen. We study a modification of this model on the square lattice, where each cluster freezes when its diameter is larger than N. We show that in the limit when N goes to infinity, the probability that the origin is still active at time t=1 is positive.