Critical branching random walk in an IID environment

Engländer János () and Sieben Nándor ()
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Engländer János: Department of Mathematics, University of Colorado, Boulder, CO-80309-0395, USA.
Sieben Nándor: Department of Mathematics and Statistics, Northern Arizona University, Flagstaff, AZ-86011, USA.

Monte Carlo Methods and Applications, 2011, vol. 17, issue 2, 169-193

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.

Keywords: Branching random walk; catalytic branching; mild obstacles; critical branching; random environment; simulation (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1515/mcma.2011.008

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