相关论文: Extreme value statistics of correlated random vari…

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…

We show that generalised extreme value statistics -the statistics of the k-th largest value among a large set of random variables- can be mapped onto a problem of random sums. This allows us to identify classes of non-identical and…

Extreme value (EV) statistics of correlated systems are widely investigated in many fields, spanning the spectrum from weather forecasting to earthquake prediction. Does the unavoidable discrete sampling of a continuous correlated…

We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…

These notes are based on lectures delivered by G. Schehr at the XVIth School on Fundamental Problems in Statistical Physics (FPSP), held in Oropa (Italy) from 30 June to 11 July 2025. After a brief introduction to extreme value statistics…

While averages and typical fluctuations often play a major role to understand the behavior of a non-equilibrium system, this nonetheless is not always true. Rare events and large fluctuations are also pivotal when a thorough analysis of the…

We study the extreme value distribution of stochastic processes modeled by superstatistics. Classical extreme value theory asserts that (under mild asymptotic independence assumptions) only three possible limit distributions are possible,…

We study the statistics of the maximum and minimum of a set of $N$ random variables whose dynamical and statistical properties fall within the scope of infinite ergodic theory. These non-stationary yet recurrent systems are described, in…

Fluctuations of global additive quantities, like total energy or magnetization for instance, can in principle be described by statistics of sums of (possibly correlated) random variables. Yet, it turns out that extreme values (the largest…

Extreme value statistics provides accurate estimates for the small occurrence probabilities of rare events. While theory and statistical tools for univariate extremes are well-developed, methods for high-dimensional and complex data sets…

We study distributional robustness in the context of Extreme Value Theory (EVT). We provide a data-driven method for estimating extreme quantiles in a manner that is robust against incorrect model assumptions underlying the application of…

We study the limit distribution of the largest fitness for two models of weakly correlated and identically distributed random fitnesses. The correlated fitness is given by a linear combination of a fixed number of independent random…

We study analytically the distribution of the minimum of a set of hierarchically correlated random variables $E_1$, $E_2$, $...$, $E_N$ where $E_i$ represents the energy of the $i$-th path of a directed polymer on a Cayley tree. If the…

A pedagogical account of some aspects of Extreme Value Statistics (EVS) is presented from the somewhat non-standard viewpoint of Large Deviation Theory. We address the following problem: given a set of $N$ i.i.d. random variables…

Extreme value analysis (EVA) is a statistical method that studies the properties of extreme values of datasets, crucial for fields like engineering, meteorology, finance, insurance, and environmental science. EVA models extreme events using…

The low temperature physics of disordered systems is governed by the statistics of extremely low energy states. It is thus rather important to discuss the possible universality classes for extreme value statistics. We compare the usual…

Extreme values and the tail behavior of probability distributions are essential for quantifying and mitigating risk in complex systems of all kinds. In multivariate settings, accounting for correlations is crucial. Although extreme value…

We investigate extreme value theory for physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin models. As shown previously, a special feature is that the…

An exact analytical description of extreme intensity statistics in complex random states is derived. These states have the statistical properties of the Gaussian and Circular Unitary Ensemble eigenstates of random matrix theory. Although…

This paper unifies and extends results on a class of multivariate Extreme Value (EV) models studied by Hougaard, Crowder, and Tawn. In these models both unconditional and conditional distributions are EV, and all lower-dimensional marginals…