ubl
Das parabolische Anderson-Modell mit Be- und Entschleunigung
2011-01-24
[Electronic ed.]
prv
Universitätsbibliothek Leipzig
Universitätsbibliothek Leipzig, Leipzig
Fakultät für Mathematik und Informatik
female
Leipzig
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.
519
Parabolisches Anderson-Modell, Momentenasymptotik, Variationsformeln, be- und entschleunigte Diffusion, Große Abweichungen, Irrfahrten in zufälliger Landschaft
parabolic Anderson model, moment asymptotics, variational formulas, accelerated and decelerated diffusion, large deviations, random walk in random scenery
urn:nbn:de:bsz:15-qucosa-63649
Universität Leipzig
dgg
Universität Leipzig, Leipzig
Sylvia
Schmidt
1978-12-13
aut
Wolfgang
König
Prof. Dr.
dgs
rev
Peter
Mörters
Prof. Dr.
rev
ger
2010-07-13
2010-12-15
born digital
Sylvia Schmidt
Sylvia.Schmidt@math.uni-leipzig.de
doctoral_thesis