Critical branching random walk in an IID environment

János Engländer, Nandor Sieben

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 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.

Original languageEnglish (US)
Pages (from-to)169-193
Number of pages25
JournalMonte Carlo Methods and Applications
Volume17
Issue number2
DOIs
StatePublished - Jun 2011

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Branching Random Walk
Branching
Survival Probability
Branching Rules
Averaging
Tail
Open Problems
Simulation
High Performance
Iteration
Unit

Keywords

  • Branching random walk
  • Catalytic branching
  • Critical branching
  • Mild obstacles
  • Random environment
  • Simulation

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics

Cite this

Critical branching random walk in an IID environment. / Engländer, János; Sieben, Nandor.

In: Monte Carlo Methods and Applications, Vol. 17, No. 2, 06.2011, p. 169-193.

Research output: Contribution to journalArticle

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