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From charged polymers to random walk in random scenery. (English) Zbl 1271.60106

Rojo, Javier (ed.), Optimality. The third Erich L. Lehmann symposium. Selected papers based on the presentations at the symposium, Rice University, Houston, TX, USA, May 16–19, 2007. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 978-0-940600-77-5/pbk). Institute of Mathematical Statistics Lecture Notes - Monograph Series 57, 237-251 (2009).
Summary: We prove that two seemingly different models of random walk in random environment are generically quite close to one another. One model comes from statistical physics, and describes the behavior of a randomly charged random polymer. The other model comes from probability theory, and was originally designed to describe a large family of asymptotically self-similar processes that have stationary increments.
For the entire collection see [Zbl 1203.62003].

MSC:

60K37 Processes in random environments
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82D60 Statistical mechanics of polymers
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