2015/03/13 by Nicola Kistler, Kistler, Nicola, Marius A. Schmidt +1
Economics, Econometrics and Finance · Mathematics · #60G70 #60J80 (primary) #82B44 (secondary) #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60G70 #msc:60J80 #msc:82B44
paper · pdf · doi:10.48550/arxiv.1503.04064
12 pages, 1 figure
arxiv created 2015/03/13 · openalex publication_date 2015/03/13 · arxiv updated 2015/03/16 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
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.