Limit theorems for the maximal eigenvalues of the mean-field Hamiltonian with random potential
type: Item
instance of: scholarly article
title: Limit theorems for the maximal eigenvalues of the mean-field Hamiltonian with random potential
zbMATH Open document ID: 0956.60023
DOI: 10.1007/BF02469277
published in: Lithuanian Mathematical Journal
publication date: 2001-03-07T00:00:00Z
review text: Let \(\overline H_V:=\kappa\overline\Delta_V+ \xi(x)\), \(x\in V\subset\mathbb{Z}^\nu\), denote the mean field (Curie-Weiss) Hamiltonian with i.i.d. potential \(\xi\). Limit theorems are derived for the extreme eigenvalue of \(\overline H_V\) as \(|V|\to \infty\). The limit laws are the same as for the corresponding extremes of \(\xi\) only if either \(\xi\) is unbounded, or if \(\xi\) is bounded with ``sharp'' peaks and \(\kappa\ll 1\). Localization properties of the corresponding eigenfunctions are also studied.
Mathematics Subject Classification ID: 60F99
zbMATH DE Number: 1466094
author: Arvydas Astrauskas
MaRDI profile type: Publication
cites work: Q4695476
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description: scientific article; zbMATH DE number 1466094