Renormalization group solution of the Chutes & Ladder model

Lauren A. Ball, Alfred C.K. Farris and Stefan Boettcher

Physica A: Statistical Mechanics and its Applications, 2015, vol. 421, issue C, 171-179

Abstract: We analyze a semi-infinite one-dimensional random walk process with a biased motion that is incremental in one direction and long-range in the other. On a network with a fixed hierarchy of long-range jumps, we find with exact renormalization group calculations that there is a dynamical transition between a localized adsorption phase and an anomalous diffusion phase in which the mean-square displacement exponent depends non-universally on the Bernoulli coin. We relate these results to similar findings of unconventional phase behavior in hierarchical networks.

Keywords: Random walks; Hierarchical networks; Renormalization group; Non-universality; Persistent walks; De-localization (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:421:y:2015:i:c:p:171-179

DOI: 10.1016/j.physa.2014.11.020

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