On the tail of the branching random walk local time.

Omer AngelTom HutchcroftAntal Járai

Published in: Probability theory and related fields (2020)

Consider a critical branching random walk on Z d , d ≥ 1 , started with a single particle at the origin, and let L(x) be the total number of particles that ever visit a vertex x. We study the tail of L(x) under suitable conditions on the offspring distribution. In particular, our results hold if the offspring distribution has an exponential moment.

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