Euler Walk on a Cayley Tree

We describe two possible regimes (dynamic phases) of the Euler walk on a Cayley tree: a condensed phase and a low-density phase. In the condensed phase the area of visited sites grows as a compact domain. In the low-density phase the proportion of visited sites decreases rapidly from one generation...

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Bibliographic Details
Published in:Journal of statistical physics 2007-05, Vol.127 (3), p.629-653
Main Author: Patrick, A. E.
Format: Article
Language:English
Subjects:
Density
Domains
Physics
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Summary:We describe two possible regimes (dynamic phases) of the Euler walk on a Cayley tree: a condensed phase and a low-density phase. In the condensed phase the area of visited sites grows as a compact domain. In the low-density phase the proportion of visited sites decreases rapidly from one generation of the tree to the next. We describe in detail returns of the walker to the root and growth of the domain of visited sites in the condensed phase. We also investigate the critical behaviour of the model on the line separating the two regimes.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-007-9281-5