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

Chen, Xia; Khoshnevisan, Davar

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

Keywords:

polymer measures; random walk in random scenery