Related papers: Extreme value problems in Random Matrix Theory and…
We quantify the large deviations of Gaussian extreme value statistics on closed convex sets in d-dimensional Euclidean space. The asymptotics imply that the extreme value distribution exhibits a rate function that is a simple quadratic…
In nature or societies, the power-law is present ubiquitously, and then it is important to investigate the mathematical characteristics of power-laws in the recent era of big data. In this paper we prove the superposition of non-identical…
This paper investigates the use of extreme value theory for modelling the distribution of demand-net-of-wind for capacity adequacy assessment. Extreme value theory approaches are well-established and mathematically justified methods for…
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…
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…
We apply Tsallis's q-indexed nonextensive entropy to formulate a random matrix theory (RMT), which may be suitable for systems with mixed regular-chaotic dynamics. We consider the super-extensive regime of q < 1. We obtain analytical…
The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law-invariant coherent risk measures only consists of…
For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…
In this paper, we consider the singular values and singular vectors of finite, low rank perturbations of large rectangular random matrices. Specifically, we prove almost sure convergence of the extreme singular values and appropriate…
We study the statistics of height and balanced height in the binary search tree problem in computer science. The search tree problem is first mapped to a fragmentation problem which is then further mapped to a modified directed polymer…
We numerically study the extreme-value statistics of the Schmidt eigenvalues of reduced density matrices obtained from the ergodic eigenstates. We start by exploring the extreme value statistics of the ultrametric random matrices and then…
The paper deals with distribution of singular values of product of random matrices arising in the analysis of deep neural networks. The matrices resemble the product analogs of the sample covariance matrices, however, an important…
During last two decades it has been discovered that the statistical properties of a number of microscopically rather different random systems at the macroscopic level are described by {\it the same} universal probability distribution…
Supersymmetry is nowadays indispensable for many problems in Random Matrix Theory. It is presented here with an emphasis on conceptual and structural issues. An introduction to supermathematics is given. The Hubbard-Stratonovich…
A systematic analysis of large scale fluctuations in the low temperature pinned phase of a directed polymer in a random potential is described. These fluctuations come from rare regions with nearly degenerate ``ground states''. The…
An exact analytical description of extreme intensity statistics in complex random states is derived. These states have the statistical properties of the Gaussian and Circular Unitary Ensemble eigenstates of random matrix theory. Although…
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…
We study the limiting distribution of critical points and extrema of random spherical harmonics, in the high energy limit. In particular, we first derive the density functions of extrema and saddles; we then provide analytic expressions for…
Extreme value theory for chaotic dynamical systems is a rapidly expanding area of research. Given a system and a real function (observable) defined on its phase space, extreme value theory studies the limit probabilistic laws obeyed by…
We consider the problem of rational decision making in the presence of nonlinear constraints. By using tools borrowed from spin glass and random matrix theory, we focus on the portfolio optimisation problem. We show that the number of…