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2015 From Derrida's random energy model to branching random walks: from 1 to 3
Marius Schmidt, Nicola Kistler
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Electron. Commun. Probab. 20: 1-12 (2015). DOI: 10.1214/ECP.v20-4189

Abstract

We study the extremes of a class of Gaussian fields with in-built hierarchical structure. The number of scales in the underlying trees depends on a parameter $\alpha \in \left[0,1\right]$: choosing $\alpha=0$ yields the random energy model by Derrida (REM), whereas $\alpha=1$ corresponds to the branching random walk (BRW). When the parameter $\alpha$ increases, the level of the maximum of the field decreases smoothly from the REM- to the BRW-value. However, as long as $\alpha<1$ strictly, the limiting extremal process is always Poissonian.

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Marius Schmidt. Nicola Kistler. "From Derrida's random energy model to branching random walks: from 1 to 3." Electron. Commun. Probab. 20 1 - 12, 2015. https://doi.org/10.1214/ECP.v20-4189

Information

Accepted: 10 June 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1321.60111
MathSciNet: MR3358969
Digital Object Identifier: 10.1214/ECP.v20-4189

Subjects:
Primary: 60J80
Secondary: 60G70 , 82B44

Keywords: Extremal process , Extreme value theory , Gaussian hierarchical fields

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