From Derrida's random energy model to branching random walks: from 1 to 3
Probability
2015-03-16 v1
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 [0,1]: 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.
Keywords
Cite
@article{arxiv.1503.04064,
title = {From Derrida's random energy model to branching random walks: from 1 to 3},
author = {Nicola Kistler and Marius A. Schmidt},
journal= {arXiv preprint arXiv:1503.04064},
year = {2015}
}
Comments
12 pages, 1 figure