Renormalization Group Solution of the Chutes&Ladder Model
arXiv:1410.2092 · doi:10.1016/j.physa.2014.11.020
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.
arXiv comment7 pages, RevTex4.1; for related information, see http://www.physics.emory.edu/faculty/boettcher/
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