Spectral asymptotics of random operators
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 \(\lambda_{\ell}=\ell^{\rho}\lambda_ 1\), \(h=1\).
scientific article; zbMATH DE number 4099809
scientific article