# 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}
}
• 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…

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## References

SHOWING 1-10 OF 37 REFERENCES
Branching Random Walk in a Catalytic Medium. I. Basic Equations
• Mathematics
• 2000
We consider a continuous-time branching random walk on the integer lattice ℤd (d ≥ 1 ) with a finite number of branching sources, or catalysts. The random walk is assumed to be spatially homogeneous
Limit Theorem for Critical Catalytic Branching Random Walks
• Mathematics
• 2005
A continuous time branching random walk on the lattice {\bf Z} is considered in which individuals may produce children at the origin only. Assuming that the underlying Markov random walk is
Quenched law of large numbers for branching Brownian motion in a random medium
We study a spatial branching model, where the underlying motion is d-dimensional (d ≥ 1) Brownian motion and the branching rate is affected by a random collection of reproduction suppressing sets
Brownian motion, obstacles, and random media
This book is aimed at graduate students and researchers. It provides an account for the non-specialist of the circle of ideas, results and techniques, which grew out in the study of Brownian motion
Escape Probabilities for Branching Brownian Motion Among Soft Obstacles
• Mathematics
• 2010
We derive asymptotics for the quenched probability that a critical branching Brownian motion killed at a small rate ε in Poissonian obstacles exits from a large domain. Results are formulated in
Branching Random Walk with Catalysts
• Mathematics
• 2003
Shnerb et al. (2000), (2001) studied the following system of interacting particles on $\Bbb Z^d$: There are two kinds of particles, called $A$-particles and $B$-particles. The $A$-particles perform
A Review on Spatial Catalytic Branching
We review some results on spatial branching processes X in random media . The local branching rate or law depends on the medium that may vary in space and time and can be random. The main emphasis
Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
• Computer Science, Mathematics
TOMC
• 1998
A new algorithm called Mersenne Twister (MT) is proposed for generating uniform pseudorandom numbers, which provides a super astronomical period of 2 and 623-dimensional equidistribution up to 32-bit accuracy, while using a working area of only 624 words.
An MPI Implementation of a Self-Submitting Parallel Job Queue
• Computer Science
International Journal of Parallel Programming
• 2012
A simple and easy to apply methodology for using high-level self-submitting parallel job queues in an MPI environment, and a library of functions, MPQueue, which can solve large problems in parallel without being an expert in MPI.