The Parabolic Anderson Model with Acceleration and Deceleration

Details The Parabolic Anderson Model with Acceleration and Deceleration The Parabolic Anderson Model with Acceleration and Deceleration

2010-10-16

arxiv.org/abs/1010.3353v1

Mathematics

Probability

19 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The Parabolic Anderson Model with Acceleration and Deceleration does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Parabolic Anderson Model with Acceleration and Deceleration, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Parabolic Anderson Model with Acceleration and Deceleration will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-181980