Related papers: Extreme value theory for constrained physical syst…

Currently available models for spatial extremes suffer either from inflexibility in the dependence structures that they can capture, lack of scalability to high dimensions, or in most cases, both of these. We present an approach to spatial…

In this paper, we discuss the emergence of extreme events in a parametrically driven non-polynomial mechanical system with a velocity-dependent potential. We confirm the occurrence of extreme events from the probability distribution…

It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but…

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…

Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…

Motivated by the psychological literature on the "peak-end rule" for remembered experience, we perform an analysis within a random walk framework of a discrete choice model where agents' future choices depend on the peak memory of their…

Although the fundamental probabilistic theory of extremes has been well developed, there are many practical considerations that must be addressed in application. The contribution of this thesis is four-fold. The first concerns the choice of…

Inference over tails is usually performed by fitting an appropriate limiting distribution over observations that exceed a fixed threshold. However, the choice of such threshold is critical and can affect the inferential results. Extreme…

Data-driven anomaly detection methods typically build a model for the normal behavior of the target system, and score each data instance with respect to this model. A threshold is invariably needed to identify data instances with high (or…

A distributional route to Gaussianity, associated with the concept of Conservative Mixing Transformations in ensembles of random vector-valued variables, is proposed. This route is completely different from the additive mechanism…

Motivated by the analysis of extreme rainfall data, we introduce a general Bayesian hierarchical model for estimating the probability distribution of extreme values of intermittent random sequences, a common problem in geophysical and…

Rare events in stochastic processes with heavy-tailed distributions are controlled by the big jump principle, which states that a rare large fluctuation is produced by a single event and not by an accumulation of coherent small deviations.…

We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- direct cascading or fragmentation, spatial dynamics, and external driving -- are combined in a classical age-dependent…

The extreme value statistics of active matter offer significant insight into their unique properties. A phase transition has recently been reported in a model of branching run-and-tumble particles, describing the spatial spreading of an…

The emergence of a predominant phenotype within a cell population is often triggered by a rare accumulation of DNA mutations in a single cell. For example, tumors may be initiated by a single cell in which multiple mutations cooperate to…

We present a novel statistical treatment, the "metastatistics of extreme events", for calculating the frequency of extreme events. This approach, which is of general validity, is the proper statistical framework to address the problem of…

This thesis is devoted to the study of extreme value statistics in stochastic processes and their applications. In the first part, we obtain exact analytical results on the extreme value statistics of both discrete-time and continuous-time…

Extreme value theory is part and parcel of any study of order statistics in one dimension. Our aim here is to consider such large sample theory for the maximum distance to the origin, and the related maximum "interpoint distance," in…

Understanding and predicting uncertain things are the central themes of scientific evolution. Human beings revolve around these fears of uncertainties concerning various aspects like a global pandemic, health, finances, to name but a few.…

We review the question of the extreme values attained by a random process. We relate it to level crossings either to one boundary (first-passage problems) and two boundaries (escape problems). The extremes studied are the maximum, the…