相关论文: Free extreme values

Max-stable random fields play a central role in modeling extreme value phenomena. We obtain an explicit formula for the conditional probability in general max-linear models, which include a large class of max-stable random fields. As a…

We theoretically and numerically investigated the threshold network model with a generic weight function where there were a large number of nodes and a high threshold. Our analysis was based on extreme value theory, which gave us a…

This work builds on our previous developments regarding a notion of freeness for tensors. We aim to establish a tensorial free convolution for compactly supported measures. First, we define higher-order analogues of the semicircular (or…

In a previous paper (called "Rectangular random matrices. Related covolution"), we defined, for $\lambda \in [0,1]$, the rectangular free convolution with ratio $\lambda$. Here, we investigate the related notion of infinite divisiblity,…

The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…

The paper proposes another extension of the extremal principle. A new extremality model involving collections of arbitrary families of sets is studied. It generalizes the conventional model based on linear translations of given sets as well…

We prove limit theorems of an entirely new type for certain long memory regularly varying stationary infinitely divisible random processes. These theorems involve multiple phase transitions governed by how long the memory is. Apart from one…

This paper describes the quality of convergence to an infinitely divisible law relative to free multiplicative convolution. We show that convergence in distribution for products of identically distributed and infinitesimal free random…

We consider the extreme value theory of a hyperbolic toral automorphism $T: \mathbb{T}^2 \to \mathbb{T}^2$ showing that if a H\"older observation $\phi$ which is a function of a Euclidean-type distance to a non-periodic point $\zeta$ is…

Preferential attachment probabilities scheme appear in the context of scale free random graphs [1],[2]. In this work we present preferential attachment probabilities scheme as a sequence of dependent Bernoulli random variables and we give…

Asymptotic laws of records values have usually been investigated as limits in type. In this paper, we use functional representations of the tail of cumulative distribution functions in the extreme value domain of attraction to directly…

Using the technique developed in approximation theory, we construct examples of exponential families of infinitely divisible laws which can be viewed as deformations of the normal, gamma, and Poisson exponential families. Replacing the…

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…

We consider extremal eigenvalues of sparse random matrices, a class of random matrices including the adjacency matrices of Erd\H{o}s-R\'{e}nyi graphs $\mathcal{G}(N,p)$. Recently, it was shown that the leading order fluctuations of extremal…

In this paper we develop new extremal principles in variational analysis that deal with finite and infinite systems of convex and nonconvex sets. The results obtained, unified under the name of tangential extremal principles, combine primal…

Moments are expectation values of products of powers of position and momentum, taken over quantum states (or averages over a set of classical particles). For free particles, the evolution in the quantum case is closely related to that of a…

We extend the scope of the dynamical theory of extreme values to cover phenomena that do not happen instantaneously, but evolve over a finite, albeit unknown at the onset, time interval. We consider complex dynamical systems, composed of…

The maxima and the minima of a randomly stopped sample of a random variable, $X$, together with two newly defined random variables that make $X$ into the maxima or minima of a randomly stopped sample of them, can be used to define…

We study non-stationary stochastic processes arising from sequential dynamical systems built on maps with a neutral fixed points and prove the existence of Extreme Value Laws for such processes. We use an approach developed in \cite{FFV16},…

We give a brief account of application of extreme value theory in dynamical systems by using perturbation techniques associated to the transfer operator. We will apply it to the baker's map and we will get a precise formula for the extremal…