Random environmental potentials (Gaussian or semi-selfsimilar Lévy) almost surely yield noncompact Markov semigroups with zero essential spectral bottom, destroying deterministic confinement.
Kˆ ono, Asymptotic behavior of sample functions of Gaussian random fields,J
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Essential spectrum for Brox-type diffusion processes
Random environmental potentials (Gaussian or semi-selfsimilar Lévy) almost surely yield noncompact Markov semigroups with zero essential spectral bottom, destroying deterministic confinement.