Related papers: Extreme value theory for constrained physical syst…
In this paper we are concerned with the analysis of heavy-tailed data when a portion of the extreme values is unavailable. This research was motivated by an analysis of the degree distributions in a large social network. The degree…
Aggregation processes with an arbitrary number of conserved quantities are investigated. On the mean-field level, an exact solution for the size distribution is obtained. The asymptotic form of this solution exhibits nontrivial ``double''…
Noncolliding diffusion processes reported in the present paper are $N$-particle systems of diffusion processes in one-dimension, which are conditioned so that all particles start from the origin and never collide with each other in a finite…
The last decade has seen numerous record-shattering heatwaves in all corners of the globe. In the aftermath of these devastating events, there is interest in identifying worst-case thresholds or upper bounds that quantify just how hot…
The classical multivariate extreme value theory tries to capture the extremal dependence between the components under a multivariate domain of attraction condition and it requires each of the components to be in the domain of attraction of…
We consider globally invertible and piecewise contracting maps in higher dimensions and we perturb them with a particular kind of noise introduced by Lasota and Mackey. We got random transformations which are given by a stationary process:…
We introduce the extremal range, a local statistic for studying the spatial extent of extreme events in random fields on $\mathbb{R}^d$. Conditioned on exceedance of a high threshold at a location $s$, the extremal range at $s$ is the…
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…
In this note, we obtain verifiable sufficient conditions for the extreme value distribution for a certain class of skew product extensions of non-uniformly hyperbolic base maps. We show that these conditions, formulated in terms of the…
The univariate extreme value theory deals with the convergence in type of powers of elements of sequences of cumulative distribution functions on the real line when the power index gets infinite. In terms of convergence of random variables,…
We study the distribution of the occurrence of rare patterns in sufficiently mixing Gibbs random fields on the lattice $\mathbb{Z}^d$, $d\geq 2$. A typical example is the high temperature Ising model. This distribution is shown to converge…
This work employs variational techniques to revisit and expand the construction and analysis of extreme value processes. These techniques permit a novel study of spatial statistics of the location of minimizing events. We develop integral…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
A central problem in uncertainty quantification is how to characterize the impact that our incomplete knowledge about models has on the predictions we make from them. This question naturally lends itself to a probabilistic formulation, by…
Several theoretical results concerning event-by-event fluctuations are discussed: (1) a role of the global conservation laws and concept of statistical ensembles; (2) strongly intensive measures are introduced; they give a possibility to…
Extremal principles are fundamental in our interpretation of phenomena in nature. One of the best known examples is the second law of thermodynamics, governing most physical and chemical systems and stating the continuous increase of…
We investigate energy diffusion in long-range interacting spin systems, where the interaction decays algebraically as $V(r) \propto r^{-\alpha}$ with the distance $r$ between the sites. We consider prototypical spin systems, the transverse…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
We propose a new class of extreme-value copulas which are extreme-value limits of conditional normal models. Conditional normal models are generalizations of conditional independence models, where the dependence among observed variables is…
We explain the connection between the Gumbel limit for diffusion exit times and the theory of extreme values.