2010/03/25 by János Engländer, Janos Englander, Englander, Janos +3
Computer Science · Mathematics · #Branching (polymer chemistry) #Branching process #Branching random walk #Cellular Automata and Applications #Chaos-based Image/Signal Encryption #Combinatorics #Discrete mathematics #Materials science #Mathematics #Physics #Random walk #Statistical physics #Statistics #Stochastic processes and statistical mechanics #math.PR #msc:60K37 #msc:P60J80
paper · pdf · doi:10.48550/arxiv.1003.4950
arxiv created 2010/03/25 · openalex publication_date 2010/03/25 · arxiv updated 2010/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Using a high performance computer cluster, we run simulations regarding an open problem about d-dimensional critical branching random walks in a random IID environment The environment is given by the rule that at every site independently, with probability p>0, there is a cookie, completely suppressing the branching of any particle located there. Abstract. The simulations suggest self averaging: the asymptotic survival probability in n steps is the same in the annealed and the quenched case; it is (2)/(qn), where q:=1-p. This particular asymptotics indicates a non-trivial phenomenon: the tail of the survival probability (both in the annealed and the quenched case) is the same as in the case of non-spatial unit time critical branching, where the branching rule is modified: branching only takes place with probability q for every particle at every iteration.