Spectral Properties of Random Non-self-adjoint Matrices and Operators

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dc.creatorDavies, E B
dc.date2000-02-19
dc.date.accessioned2026-07-07T04:33:58Z
dc.date.available2026-07-07T04:33:58Z
dc.descriptionWe describe some numerical experiments which determine the degree of spectral instability of medium size randomly generated matrices which are far from self-adjoint. The conclusion is that the eigenvalues are likely to be intrinsically uncomputable for similar matrices of a larger size. We also describe a stochastic family of bounded operators in infinite dimensions for almost all of which the eigenvectors generate a dense linear subspace, but the eigenvalues do not determine the spectrum. Our results imply that the spectrum of the non-self-adjoint Anderson model changes suddenly as one passes to the infinite volume limit.
dc.descriptionkeywords: eigenvalues, spectral instability, matrices, computability, pseudospectrum, Schroedinger operator, Anderson model
dc.identifierhttps://arxiv.org/abs/math/0002159
dc.identifierhttp://arxiv.org/abs/math/0002159
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58726
dc.subjectSpectral Theory
dc.subjectMathematical Physics
dc.subject65F15; 65F22; 15A18; 15A52; 47A75; 47B80; 60H25
dc.titleSpectral Properties of Random Non-self-adjoint Matrices and Operators
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