Critical branching random walk in an IID environment
Abstract
Using a high performance computer cluster, we run simulations regarding an open problem about ddimensional 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 \frac{2}{qn}, where q:=1p. This particular asymptotics indicates a nontrivial phenomenon: the tail of the survival probability (both in the annealed and the quenched case) is the same as in the case of nonspatial unit time critical branching, where the branching rule is modified: branching only takes place with probability q for every particle at every iteration.
 Publication:

arXiv eprints
 Pub Date:
 March 2010
 arXiv:
 arXiv:1003.4950
 Bibcode:
 2010arXiv1003.4950E
 Keywords:

 Mathematics  Probability;
 P60J80 (Primary);
 60K37 (Secondary)