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A Random Walk with Collapsing Bonds and Its Scaling Limit

Authors: Majid Hosseini a; Krishnamurthi Ravishankar a
Affiliation:   a Department of Mathematics, State University of New York at New Paltz, New Paltz, New York, USA
DOI: 10.1080/07362990701670241
Publication Frequency: 6 issues per year
Published in: journal Stochastic Analysis and Applications, Volume 26, Issue 1 January 2008 , pages 29 - 38
Formats available: HTML (English) : PDF (English)
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Abstract

We introduce a new self-interacting random walk on the integers in a dynamic random environment and show that it converges to a pure diffusion in the scaling limit. We also find a lower bound on the diffusion coefficient in some special cases. With minor changes the same argument can be used to prove the scaling limit of the corresponding walk in Zopfd.
Keywords: Dynamic random environment; Scaling limit; Self-interacting random walks
Mathematics Subject Classification: Primary 60K37; Secondary 60F17, 60G50
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