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Das parabolische Anderson-Modell mit Be- und Entschleunigung

We describe the large-time moment asymptotics for the parabolic Anderson model where the speed of the diffusion is coupled with time, inducing an acceleration or deceleration. We find a lower critical scale, below which the mass flow gets stuck. On this scale, a new interesting variational problem arises in the description of the asymptotics. Furthermore, we find an upper critical scale above which the potential enters the asymptotics only via some average, but not via its extreme values. We make out altogether five phases, three of which can be described by results that are qualitatively similar to those from the constant-speed parabolic Anderson model in earlier work by various authors. Our proofs consist of adaptations and refinements of their methods, as well as a variational convergence method borrowed from finite elements theory.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:15-qucosa-63649
Date24 January 2011
CreatorsSchmidt, Sylvia
ContributorsUniversität Leipzig, Fakultät für Mathematik und Informatik, Prof. Dr. Wolfgang König, Prof. Dr. Wolfgang König, Prof. Dr. Peter Mörters
PublisherUniversitätsbibliothek Leipzig
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
Languagedeu
Detected LanguageEnglish
Typedoc-type:doctoralThesis
Formatapplication/pdf

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