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2012 Branching random walks in time inhomogeneous environments
Ming Fang, Ofer Zeitouni
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Electron. J. Probab. 17: 1-18 (2012). DOI: 10.1214/EJP.v17-2253

Abstract

We study the maximal displacement of branching random walks in a class of time inhomogeneous environments. Specifically, binary branching random walks with Gaussian increments will be considered, where the variances of the increments change over time macroscopically. We find the asymptotics of the maximum up to an $O_P(1)$ (stochastically bounded) error, and focus on the following phenomena: the profile of the variance matters, both to the leading (velocity) term and to the logarithmic correction term, and the latter exhibits a phase transition.

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Ming Fang. Ofer Zeitouni. "Branching random walks in time inhomogeneous environments." Electron. J. Probab. 17 1 - 18, 2012. https://doi.org/10.1214/EJP.v17-2253

Information

Accepted: 19 August 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1252.60099
MathSciNet: MR2968674
Digital Object Identifier: 10.1214/EJP.v17-2253

Subjects:
Primary: 60G50
Secondary: 60J80

JOURNAL ARTICLE
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Vol.17 • 2012
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