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 (6)

• Universality Classes for Extreme Value Statistics
• Convergence in law of the minimum of a branching random walk
• Local limits of conditioned Galton-Watson trees I: the infinite spine case
• Universal Order and Gap Statistics of Critical Branching Brownian Motion
• Branching Brownian Motion Conditioned on Particle Numbers
• The harmonic measure of balls in random trees