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 (\emph{Duke Math. J.} 171(3):483--545, 2022) in the case of Gaussian multiplicative cascades.
From: Heng Ma [view email]
[v1]
Sat, 16 Aug 2025 08:46:48 UTC (354 KB)
[v2]
Tue, 21 Jul 2026 18:31:16 UTC (357 KB)
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