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arXiv · 1410.2092

Renormalization Group Solution of the Chutes&Ladder Model

Lauren A. Ball·Alfred C. K. Farris·Stefan Boettcher
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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.

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BibTeXRIS

Lauren A. Ball, Alfred C. K. Farris, Stefan Boettcher. 2014-10-08. Renormalization Group Solution of the Chutes&Ladder Model. https://doi.org/10.1016/j.physa.2014.11.020

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