## Spectral properties of random non-self-adjoint matrices and operators (2001)

Citations: | 7 - 4 self |

### BibTeX

@MISC{Davies01spectralproperties,

author = {E. B. Davies},

title = {Spectral properties of random non-self-adjoint matrices and operators},

year = {2001}

}

### OpenURL

### Abstract

We 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.