Concentration Inequalities for Branching Random Walks

Changqing Liu

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arXiv · 2509.05860

Concentration Inequalities for Branching Random Walks

Changqing Liu

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Abstract

Motivated by phase transition problems in CSPs, we prove a more general concentration inequality that retains classical sub-Gaussian tails under a mild global linear-growth condition $|S_n| < Cn$, relaxing the bounded-increment assumption to finite exponential moments and requiring neither independence nor the martingale property. We further extend it to branching random walks (BRWs), obtaining the first concentration inequality for BRWs.

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Changqing Liu. 2025-09-06. Concentration Inequalities for Branching Random Walks. https://arxiv.org/abs/2509.05860

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