Abstract:We consider a branching random walk (BRW) taking its values in the b-ary rooted tree Wb (i.e. the set of finite words written in the alphabet {1, . . . , b}, with b ≥ 2). The BRW is indexed by a critical Galton-Watson tree conditioned to have n vertices; its offspring distribution is aperiodic and is in the domain of attraction of a γ-stable law, γ ∈ (1, 2].The jumps of the BRW are those of a nearest-neighbour null-recurrent random walk on Wb (reflection at the root of Wb and otherwise: probability 1/2 to move… Show more
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