- AutorIn
- Sylvia Schmidt
- Titel
- Das parabolische Anderson-Modell mit Be- und Entschleunigung
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:15-qucosa-63649
- Datum der Einreichung
- 13.07.2010
- Datum der Verteidigung
- 15.12.2010
- Abstract (EN)
- 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.
- Freie Schlagwörter (DE)
- Parabolisches Anderson-Modell, Momentenasymptotik, Variationsformeln, be- und entschleunigte Diffusion, Große Abweichungen, Irrfahrten in zufälliger Landschaft
- Freie Schlagwörter (EN)
- parabolic Anderson model, moment asymptotics, variational formulas, accelerated and decelerated diffusion, large deviations, random walk in random scenery
- Klassifikation (DDC)
- 519
- GutachterIn
- Prof. Dr. Wolfgang König
- Prof. Dr. Peter Mörters
- BetreuerIn
- Prof. Dr. Wolfgang König
- Den akademischen Grad verleihende / prüfende Institution
- Universität Leipzig, Leipzig
- URN Qucosa
- urn:nbn:de:bsz:15-qucosa-63649
- Veröffentlichungsdatum Qucosa
- 24.01.2011
- Dokumenttyp
- Dissertation
- Sprache des Dokumentes
- Deutsch