Branching random walks conditioned on rarely survival
Probability
2021-11-24 v1
Abstract
In this paper, we show that a Galton-Watson tree conditioned to have a fixed number of particles in generation converges in distribution as , 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.
Cite
@article{arxiv.2103.08283,
title = {Branching random walks conditioned on rarely survival},
author = {Tianyi Bai and Pierre Rousselin},
journal= {arXiv preprint arXiv:2103.08283},
year = {2021}
}