Almost sure central limit theorem for branching random walks in random environment

Details Almost sure central limit theorem for branching random walks in random environment Almost sure central limit theorem for branching random walks in random environment

2011-01-06

arxiv.org/abs/1101.1176v1

Annals of Applied Probability 2011, Vol. 21, No. 1, 351-373

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AAP699 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/10-AAP699

We consider the branching random walks in $d$-dimensional integer lattice with time--space i.i.d. offspring distributions. Then the normalization of the total population is a nonnegative martingale and it almost surely converges to a certain random variable. When $d\geq3$ and the fluctuation of environment satisfies a certain uniform square integrability then it is nondegenerate and we prove a central limit theorem for the density of the population in terms of almost sure convergence.

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