相关论文: Universality Classes for Extreme Value Statistics

The universality of small scales, a cornerstone of turbulence, has been nominally confirmed for low-order mean-field statistics, such as the energy spectrum. However, small scales exhibit strong intermittency, exemplified by formation of…

In order to better fit real-world datasets, studying asymmetric distribution is of great interest. In this work, we derive several mathematical properties of a general class of asymmetric distributions with positive support which shows up…

We present the methods employed by team `Uniofbathtopia' as part of the Data Challenge organised for the 13th International Conference on Extreme Value Analysis (EVA2023), including our winning entry for the third sub-challenge. Our…

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…

This study provides a summary of the theory which enables the analysis of extreme values, i.e., of measurements acquired from the observation of extraordinary/rare physical phenomena. The formalism is developed in a transparent way,…

Extreme value theory for univariate and low-dimensional observations has been explored in considerable detail, but the field is still in an early stage regarding high-dimensional settings. This paper focuses on H\"usler-Reiss models, a…

Extreme values of real phenomena are events that occur with low frequency, but can have a large impact on real life. These are, in many practical problems, high-dimensional by nature (e.g. Tawn, 1990; Coles and Tawn, 1991). To study these…

Superstatistics is a framework in nonequilibrium statistical mechanics that successfully describes a wide variety of complex systems, including hydrodynamic turbulence, weakly-collisional plasmas, cosmic rays, power grid fluctuations, among…

Uniform convergence rates are provided for asymptotic representations of sample extremes. These bounds which are universal in the sense that they do not depend on the extreme value index are meant to be extended to arbitrary samples…

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,…

Randomness is ubiquitous in many applications across data science and machine learning. Remarkably, systems composed of random components often display emergent global behaviors that appear deterministic, manifesting a transition from…

The statistical properties of turbulence are considered to be universal at sufficiently small length scales, i. e., independent of boundary conditions and large-scale forces acting on the fluid. Analyzing data from numerical simulations of…

We analyze the stochastic scaling laws arising in the invicid limit of the decaying solutions of the Burgers equation. The linear scaling of the velocity structure functions is shown to reflect the domination by shocks of the long-time…

We present the results of a percolation-like model that has been restricted compared to standard percolation models in the sense that we do not allow finite sized clusters to break up once they have formed. We calculate the critical…

In this paper, we analyze several instrumental records of temperatures at different locations by using new techniques originally developed for the analysis of extreme values of dynamical systems. We show that they have the same recurrence…

We give conditions to prove the existence of an Extremal Index for general stationary stochastic processes by detecting the presence of one or more underlying periodic phenomena. This theory, besides giving general useful tools to identify…

We consider universal aspects of two problems: (i) the slow purification of a large number of qubits by repeated quantum measurements, and (ii) the singular value structure of a product ${m_t m_{t-1}\ldots m_1}$ of many large random…

The object of this paper is twofold. From one side we study the dichotomy, in terms of the Extremal Index of the possible Extreme Value Laws, when the rare events are centred around periodic or non periodic points. Then we build a general…

Combining strengths from deep learning and extreme value theory can help describe complex relationships between variables where extreme events have significant impacts (e.g., environmental or financial applications). Neural networks learn…

This paper is concerned with the limit theory of the extreme order statistics derived from random walks. We establish the joint convergence of the order statistics near the minimum of a random walk in terms of the Feller chains. Detailed…