Left Tail of the Derivative Martingale in a Gaussian BRW in the Entire Subcritical Regime
arXiv:2508.11983
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.
22 pages, 2 figures; comments are welcome!