Mathematics – Probability
Scientific paper
2010-10-19
Mathematics
Probability
In honour of J\"urgen G\"artner on the occasion of his 60th birthday, 27 pages. References updated
Scientific paper
We review some old and prove some new results on the survival probability of a random walk among a Poisson system of moving traps on Z^d, which can also be interpreted as the solution of a parabolic Anderson model with a random time-dependent potential. We show that the annealed survival probability decays asymptotically as e^{-\lambda_1\sqrt{t}} for d=1, as e^{-\lambda_2 t/\log t} for d=2, and as e^{-\lambda_d t} for d>= 3, where \lambda_1 and \lambda_2 can be identified explicitly. In addition, we show that the quenched survival probability decays asymptotically as e^{-\tilde \lambda_d t}, with \tilde \lambda_d>0 for all d>= 1. A key ingredient in bounding the annealed survival probability is what is known in the physics literature as the Pascal principle, which asserts that the annealed survival probability is maximized if the random walk stays at a fixed position. A corollary of independent interest is that the expected cardinality of the range of a continuous time symmetric random walk increases under perturbation by a deterministic path.
Drewitz Alexander
Gärtner Jürgen
Ramirez Alejandro F.
Sun Rongfeng
No associations
LandOfFree
Survival Probability of a Random Walk Among a Poisson System of Moving Traps 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 Survival Probability of a Random Walk Among a Poisson System of Moving Traps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Survival Probability of a Random Walk Among a Poisson System of Moving Traps will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-269222