Spectral asymptotics of random operators
type: Item
instance of: scholarly article
title: Spectral asymptotics of random operators
zbMATH Open document ID: 0672.35053
DOI: 10.1007/BF01138848
published in: Mathematical Notes
publication date: 1988-01-01T00:00:00Z
review text: For a random self-adjoint elliptic differential operator A in \({\mathbb{R}}^ d\) are derived high-frequency, low-frequency and semiclassical asymptotics of the density of states \(N_ h(\lambda)\). Moreover for a similar second-order operator in a domain \(V_{\ell}=\ell V_ 1\) are derived asymptotics of an eigenvalue counting function \(N_{V_{\ell}}(\lambda_{\ell})\) as \(\ell \to \infty\) where \(V_ 1\) is a bounded domain with a smooth boundary (and a Dirichlet boundary condition) and \(\lambda_{\ell}=\ell^{\rho}\lambda_ 1\), \(h=1\).
Mathematics Subject Classification ID: 35P20
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 4099809
zbMATH Keywords: random
zbMATH Keywords: self-adjoint
zbMATH Keywords: high-frequency
zbMATH Keywords: low-frequency
zbMATH Keywords: semiclassical asymptotics
zbMATH Keywords: density of states
zbMATH Keywords: eigenvalue
zbMATH Keywords: counting function
zbMATH Keywords: smooth boundary
zbMATH Keywords: Dirichlet boundary condition
author: Serguei M. Kozlov
MaRDI profile type: Publication
cites work: Q3854075
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full work available at URL: https://doi.org/10.1007/bf01138848
OpenAlex ID: W2064222714
description: scientific article; zbMATH DE number 4099809