Tail Asymptotics for the Total Progeny of the Criti- Cal Killed Branching Random Walk
نویسنده
چکیده
We look at the branching random walk on R+ killed below zero. Let b ≥ 2 be a deterministic integer which represents the number of children of the branching random walk, and x ≥ 0 be the position of the (unique) ancestor. We introduce the rooted b-ary tree T , and we attach at every vertex u except the root an independent random variable Xu picked from a common distribution (we denote by X a generic random variable having this distribution). We define the position of the vertex u by S(u) := x + ∑
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