Large deviation estimates for branching random walks

TL;DR

This paper studies the probabilities of rare events in a branching random walk that drifts to negative infinity, establishing key probabilistic laws for the time it takes to reach certain thresholds.

Contribution

It provides new large deviation estimates and proves the law of large numbers and central limit theorem for the first passage time in this setting.

Findings

Law of large numbers for first passage time

Central limit theorem for first passage time

Large deviation estimates for the process

Abstract

We consider the branching random walk drifting to $-\infty$ and we investigate large deviations-type estimates for the first passage time. We prove the corresponding law of large numbers and the central limit theorem.