The state density of elliptic operators with random potentials

Summary The existence of the state density N() is established for certain linear elliptic coercive selfadjoint operators subject to perturbation by a unbounded random potential and its asymptotic properties discussed as (and for certain Gaussian perturbations as — ). The estimates depend on recent worlc by Métivier on the approximation numbers of the classical Sobolev spaces.The research of the author was supported by F.I.N.E.P. at U.F.R.G.S. under contract B/31/79/183/00/00 and by the CNPq.