Euler Walk on a Cayley Tree

Details Euler Walk on a Cayley Tree Euler Walk on a Cayley Tree

2007-06-21

arxiv.org/abs/0706.3161v1

Journal of Statistical Physics, vol. 127, No. 3, May 2007, pp. 629-653

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1007/s10955-007-9281-5

We show that the Euler walk on a Cayley tree exhibits two regimes (dynamic phases): a condensed phase and a low-density phase. In the condensed phase the self-organized area grows as a compact domain. In the low-density phase the proportion of self-organized (visited) nodes decreases rapidly from one generation of the tree to the next. We describe in detail returns of the Euler walk to the root and growth of the self-organized domain in the condensed phase. We also investigate the critical behaviour of the Euler walk at the point separating the two regimes.

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