• DOI:10.1515/mcma.2011.008
• Corpus ID: 15613416

Critical branching random walk in an IID environment

@inproceedings{Englnder2011CriticalBR,
  title={Critical branching random walk in an IID environment},
  author={J{\'a}nos Engl{\"a}nder and N{\'a}ndor Sieben},
  booktitle={Monte Carlo Methods Appl.},
  year={2011}
}

• J. Engländer, Nándor Sieben
• Published in Monte Carlo Methods Appl. 25 March 2010
• Mathematics

Abstract 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, 1], there is a cookie, completely suppressing the branching of any particle located there. The simulations suggest self averaging: the asymptotic survival probability in n steps is the same in the annealed and the quenched case; it is , 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.