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- W2902499341 abstract "Given a branching random walk on $${mathbb {R}}$$ started from the origin, where the tail of the branching law decays at least exponentially fast and the offspring number is at least one, let $$Z_n(cdot )$$ be the counting measure which counts the number of individuals at the n-th generation located in a given set. Under some mild conditions, it is known (Biggins in Stoch. Process. Appl. 34:255–274, 1990) that for any interval $$Asubset {mathbb {R}}$$ , $$frac{Z_n(sqrt{n}A)}{Z_n({mathbb {R}})}$$ converges a.s. to $$nu (A)$$ , where $$nu $$ is the standard Gaussian measure. In this work, we investigate the convergence rates of $$begin{aligned} {mathbb {P}}left( frac{Z_n(sqrt{n}A)}{Z_n({mathbb {R}})}-nu (A)>Delta right) , end{aligned}$$ for $$Delta in (0, 1-nu (A))$$ . We consider both the Schröder case, where the offspring number could be one, and the Böttcher case, where the offspring number is at least two." @default.
- W2902499341 created "2018-12-11" @default.
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- W2902499341 date "2018-12-01" @default.
- W2902499341 modified "2023-09-26" @default.
- W2902499341 title "On large deviation probabilities for empirical distribution of supercritical branching random walks with unbounded displacements" @default.
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- W2902499341 doi "https://doi.org/10.1007/s00440-018-0891-4" @default.
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