English

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 nn converges in distribution as nn\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.

Keywords

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}
}
R2 v1 2026-06-24T00:09:46.730Z