Extreme value statistics of correlated random variables: a pedagogical review - Archive ouverte HAL Access content directly
Journal Articles Physics Reports Year : 2020

Extreme value statistics of correlated random variables: a pedagogical review


Extreme value statistics (EVS) concerns the study of the statistics of the maximum or the minimum of a set of random variables. This is an important problem for any time-series and has applications in climate, finance, sports, all the way to physics of disordered systems where one is interested in the statistics of the ground state energy. While the EVS of `uncorrelated' variables are well understood, little is known for strongly correlated random variables. Only recently this subject has gained much importance both in statistical physics and in probability theory. In this review, we will first recall the classical EVS for uncorrelated variables and discuss the three universality classes of extreme value limiting distribution, known as the Gumbel, Fr\'echet and Weibull distribution. We then show that, for weakly correlated random variables with a finite correlation length/time, the limiting extreme value distribution can still be inferred from that of the uncorrelated variables using a renormalisation group-like argument. Finally, we consider the most interesting examples of strongly correlated variables for which there are very few exact results for the EVS. We discuss few examples of such strongly correlated systems (such as the Brownian motion and the eigenvalues of a random matrix) where some analytical progress can be made. We also discuss other observables related to extremes, such as the density of near-extreme events, time at which an extreme value occurs, order and record statistics, etc.
Fichier principal
Vignette du fichier
1910.10667 (1.06 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-02512248 , version 1 (16-12-2023)



Satya N. Majumdar, Arnab Pal, Gregory Schehr. Extreme value statistics of correlated random variables: a pedagogical review. Physics Reports, 2020, 840, pp.1-32. ⟨10.1016/j.physrep.2019.10.005⟩. ⟨hal-02512248⟩
55 View
41 Download



Gmail Mastodon Facebook X LinkedIn More