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Growth and spectrum of diffusions

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arxiv math/9806002 v1 pith:3BYUIBMG submitted 1998-06-01 math.SP math.APmath.DG

Lino Notarantonio This is my paper · ORCID
classification math.SPmath.APmath.DG
keywords growthspectrumbottomboundbrooksdiffusiondiffusionsessential
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abstract

We prove an upper bound on the bottom of the essential spectrum of a diffusion in term of the growth of the volume of $X$, generalizing a result by R. Brooks.

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  1. Essential spectrum for Brox-type diffusion processes

    math.PR 2026-07 accept novelty 7.0 of 10

    Random environmental potentials (Gaussian or semi-selfsimilar Lévy) almost surely yield noncompact Markov semigroups with zero essential spectral bottom, destroying deterministic confinement.

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