Branching random walks conditioned on rarely survival

Tianyi Bai; Pierre Rousselin

doi:10.1007/s10955-021-02833-y

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arXiv · 2103.08283

Branching random walks conditioned on rarely survival

Tianyi Bai·Pierre Rousselin

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Abstract

In this paper, we show that a Galton-Watson tree conditioned to have a fixed number of particles in generation $n$ converges in distribution as $n\rightarrow\infty$, and with this tool we study the span and gap statistics of a branching random walk on such trees, which is the discrete version of Ramola, Majumdar and Schehr 2015, generalized to arbitrary offspring and displacement distributions with moment constraints.

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Tianyi Bai, Pierre Rousselin. 2021-03-15. Branching random walks conditioned on rarely survival. https://doi.org/10.1007/s10955-021-02833-y

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