Branching random walks conditioned on rarely survival

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 $n\to \infty$, 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.

References in corpus (2)

• Universal Order and Gap Statistics of Critical Branching Brownian Motion
• Branching Brownian Motion Conditioned on Particle Numbers