Co-author(s) :

Priezzhev Viechaslav

Abstract:

A recurrent state of the rotor-routing process on a finite sink-free graph can be represented by a unicycle that is a connected spanning subgraph containing a unique directed cycle. We distinguish between short cycles of length 2 called 'dimers' and longer ones called 'contours'. Then the rotor-router walk performing an Euler tour on the graph generates a sequence of dimers and contours which exhibits both random and regular properties. Imposing initial conditions randomly chosen from the uniform distribution we calculate expected numbers of dimers and contours and correlation between them at two successive moments of time in the sequence. On the other hand, we prove that the excess of the number of contours over dimers is an invariant depending on planarity of the subgraph but not on initial conditions. In addition, we analyze the mean-square displacement of the rotor-router walker in the recurrent state.

Date submitted:

15.01.2014

Date accepted:

11.04.2014

Date of publication:

09.06.2014

Identifier:

oai:noad.sci.am:136153

DOI:

10.1088/1742-5468/2014/06/P06003

ISSN:

1742-5468

Language:

English

Journal or Publication Title:

Journal of Statistical Mechanics: Theory and Experiment

Volume:

2014

Number:

6

URL:

Additional Information:

vpoghos@theor.jinr.ru

Affiliation:

Institute for Informatics and Automation Problems ; Department of Automata Theory and Applications ; Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research

Country:

Armenia ; Russia

Indexing:

Scopus