A Random Walk with Collapsing Bonds and Its Scaling Limit

2006/11/24 by Majid Hosseini, Hosseini, Majid, K. Ravishankar +2
Mathematics · Physics and Astronomy · #60F17 #60K37 #Experimental and Theoretical Physics Studies #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60F17 #msc:60K37

paper · pdf · doi:10.48550/arxiv.math/0611734

10 pages

arxiv created 2006/11/24 · openalex publication_date 2006/11/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Z^d.

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