First order transition for the branching random walk at the critical parameter

DOI10.1016/j.spa.2015.09.008zbMath1384.60093arXiv1206.3835OpenAlexW1793255253MaRDI QIDQ901299

Thomas Madaule

Publication date: 23 December 2015

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.3835

zbMATH Keywords

phase transitionbranching random walkderivative martingale

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (16)

The near-critical Gibbs measure of the branching random walk ⋮ Range and critical generations of a random walk on Galton-Watson trees ⋮ Critical Liouville measure as a limit of subcritical measures ⋮ Tail asymptotics of maximums on trees in the critical case ⋮ Liouville measure as a multiplicative cascade via level sets of the Gaussian free field ⋮ Gaussian multiplicative chaos and applications: a review ⋮ Genealogy of the extremal process of the branching random walk ⋮ A revisited proof of the Seneta-Heyde norming for branching random walks under optimal assumptions ⋮ On the trajectory of an individual chosen according to supercritical Gibbs measure in the branching random walk ⋮ Lower deviation and moderate deviation probabilities for maximum of a branching random walk ⋮ 1-stable fluctuations in branching Brownian motion at critical temperature. I: The derivative martingale ⋮ Critical Brownian multiplicative chaos ⋮ On the derivative martingale in a branching random walk ⋮ On intermediate level sets of two-dimensional discrete Gaussian free field ⋮ A simple backward construction of branching Brownian motion with large displacement and applications ⋮ Late levels of nested occupancy scheme in random environment

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