Left Tail of the Derivative Martingale in a Gaussian BRW in the Entire Subcritical Regime

2025/08/16 by Xinxin Chen, Yichao Huang, Chen, Xinxin +4 · 1 citation
Mathematics · Physics and Astronomy · #Branching (polymer chemistry) #Branching process #Branching random walk #Conjecture #Gaussian #Martingale (probability theory) #Random walk #Spectral Theory in Mathematical Physics #Stochastic process #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Wiener process #math.PR

paper · pdf · doi:10.48550/arxiv.2508.11983

openalex publication_date 2025/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We establish a rather sharp two-sided estimate for the left tail probability of the derivative martingale limit in a binary Gaussian branching random walk throughout the entire subcritical regime, confirming a conjecture by Lacoin, Rhodes, and Vargas (Duke Math. J. 171(3):483--545, 2022) in the case of Gaussian multiplicative cascades.

Cited by

• Hölder type estimates for Gaussian multiplicative chaos

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