From extreme values of i.i.d. random fields to extreme eigenvalues of finite-volume Anderson Hamiltonian

DOI10.1214/15-PS252zbMath1350.60046arXiv1501.00949OpenAlexW1594550921MaRDI QIDQ331504

Arvydas Astrauskas

Publication date: 27 October 2016

Published in: Probability Surveys (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.00949

zbMATH Keywords

regular variationlocalisationrandom potentialrandom fieldsextreme value theoryextreme eigenvaluesWeibull distributiondiscrete Schrödinger operatorparabolic Anderson modelPoisson limit theoremsAnderson Hamiltonianextreme order statistics

Mathematics Subject Classification ID

Random fields (60G60) Central limit and other weak theorems (60F05) Random matrices (probabilistic aspects) (60B20) Extreme value theory; extremal stochastic processes (60G70) Strong limit theorems (60F15) Estimates of eigenvalues in context of PDEs (35P15) Random operators and equations (aspects of stochastic analysis) (60H25) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Random matrices (algebraic aspects) (15B52) Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics (82C44) Rate of growth of functions, orders of infinity, slowly varying functions (26A12)

Related Items (8)

Mass concentration and aging in the parabolic Anderson model with doubly-exponential tails ⋮ Longtime asymptotics of the two-dimensional parabolic Anderson model with white-noise potential ⋮ The parabolic Anderson model on a Galton-Watson tree revisited ⋮ Dissipation in parabolic SPDEs ⋮ On the spectral gap in the Kac-Luttinger model and Bose-Einstein condensation ⋮ Some bounds for the expectations of functions on order statistics and their applications ⋮ The parabolic Anderson model on a Galton-Watson tree ⋮ Phase transitions in asymptotically singular Anderson Hamiltonian and parabolic model

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