Ergodicity of a collective random walk on a circle
Dynamical Systems
2015-06-18 v1 Cellular Automata and Lattice Gases
Abstract
We discuss conditions for unique ergodicity of a collective random walk on a continuous circle. Individual particles in this collective motion perform independent (and different in general) random walks conditioned by the assumption that the particles cannot overrun each other. Additionally to sufficient conditions for the unique ergodicity we discover a new and unexpected way for its violation due to excessively large local jumps. Necessary and sufficient conditions for the unique ergodicity of the deterministic version of this system are obtained as well. Technically our approach is based on the interlacing property of the spin function which describes states of pairs of particles in coupled processes under study.
Keywords
Cite
@article{arxiv.1401.6287,
title = {Ergodicity of a collective random walk on a circle},
author = {Michael Blank},
journal= {arXiv preprint arXiv:1401.6287},
year = {2015}
}
Comments
20 pages, 6 figures