Related papers: Extremes and Records

The talk presented at ICMP 97 focused on the scaling limits of critical percolation models, and some other systems whose salient features can be described by collections of random lines. In the scaling limit we keep track of features seen…

The extreme statistics of time signals is studied when the maximum is measured from the initial value. In the case of independent, identically distributed (iid) variables, we classify the limiting distribution of the maximum according to…

This chapter illustrates how tools from univariate and multivariate statistics of extremes can complement classical methods used to study brain signals and enhance the understanding of brain activity and connectivity during specific…

We apply the theory of continuous time random walks to study some aspects of the extreme value problem applied to financial time series. We focus our attention on extreme times, specifically the mean exit time and the mean first-passage…

This paper introduces a new Importance Sampling scheme, called Adaptive Twisted Importance Sampling, which is adequate for the improved estimation of rare event probabilities in he range of moderate deviations pertaining to the empirical…

This is a set of four lectures devoted to simple ideas about turbulent transport, a ubiquitous non-equilibrium phenomenon. In the course similar to that given by the author in 2006 in Warwick [45], we discuss lessons which have been learned…

We consider a random walk on top of the contact process on $\mathbb{Z}^d$ with $d\geq 1$. In particular, we focus on the "contact process as seen from the random walk". Under the assumption that the infection rate of the contact process is…

Extreme value analysis is an essential methodology in the study of rare and extreme events, which hold significant interest in various fields, particularly in the context of environmental sciences. Models that employ the exceedances of…

We propose a numerical method to learn Maximum Entropy (MaxEnt) distributions with spatio-temporal constraints from experimental spike trains. This is an extension of two papers [10] and [4] who proposed the estimation of parameters where…

We present an informal discussion of some aspects of strong interactions under extreme conditions of temperature and density at an elementary level. This summarizes lectures delivered at the 2013 CERN -- Latin-American School of High-Energy…

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,…

Spatiotemporal extreme events are interesting phenomena, both from a fundamental point of view, as manifestations of complexity in dynamical systems, and for their possible applications in different research fields. Here, we present some…

The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step…

This paper deals with the Gaussian and bootstrap approximations to the distribution of the max statistic in high dimensions. This statistic takes the form of the maximum over components of the sum of independent random vectors and its…

We consider the extreme value statistics of centrally-biased random walks with asymptotically-zero drift in the ergodic regime. We fully characterize the asymptotic distribution of the maximum for this class of Markov chains lacking…

What is Statistics? Opinions vary. In fact, there is a continuous spectrum of attitudes toward statistics ranging from pure theoreticians, proving asymptotic efficiency and searching for most powerful tests, to wild practitioners, blindly…

In this work, we deal with extreme value theory in the context of continued fractions using techniques from probability theory, ergodic theory and real analysis. We give an upper bound for the rate of convergence in the Doeblin-Iosifescu…

Let $\mathbf{X}=\{X_{n}\}_{n\geq 1}$ be a sequence of stationary Gaussian variables and suppose that only some of the random variables from $\mathbf{X}$ can be observed. In this paper, by studying the limiting properties of multidimensional…

We generalize the concept of extremal index of a stationary random sequence to the series scheme of identically distributed random variables with random series sizes tending to infinity in probability. We introduce new extremal indices…

We consider a particle which moves on the x axis and is subject to a constant force, such as gravity, plus a random force in the form of Gaussian white noise. We analyze the statistics of first arrival at point $x_1$ of a particle which…