%0 Journal Article
%T Dynamical sensitivity of recurrence and transience of branching random walks
%A Sebastian M¨šller
%J Mathematics
%D 2009
%I arXiv
%X Consider a sequence of i.i.d. random variables $X_n$ where each random variable is refreshed independently according to a Poisson clock. At any fixed time $t$ the law of the sequence is the same as for the sequence at time 0 but at random times almost sure properties of the sequence may be violated. If there are such \emph{exceptional times} we say that the property is \emph{dynamically sensitive}, otherwise we call it \emph{dynamically stable}. In this note we consider branching random walks on Cayley graphs and prove that recurrence and transience are dynamically stable in the sub-and supercritical regime. While the critical case is left open in general we prove dynamical stability for a specific class of Cayley graphs. Our proof combines techniques from the theory of ranching random walks with those of dynamical percolation.
%U http://arxiv.org/abs/0907.4557v2