Ergodic properties of randomly coloured point sets
Abstract
We provide a framework for studying randomly coloured point sets in a locally compact, secondcountable space on which a metrisable unimodular group acts continuously and properly. We first construct and describe an appropriate dynamical system for uniformly discrete uncoloured point sets. For point sets of finite local complexity, we characterise ergodicity geometrically in terms of pattern frequencies. The general framework allows to incorporate a random colouring of the point sets. We derive an ergodic theorem for randomly coloured point sets with finiterange dependencies. Special attention is paid to the exclusion of exceptional instances for uniquely ergodic systems. The setup allows for a straightforward application to randomly coloured graphs.
 Publication:

arXiv eprints
 Pub Date:
 May 2010
 arXiv:
 arXiv:1005.4884
 Bibcode:
 2010arXiv1005.4884M
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematical Physics;
 37B50;
 37A30;
 37A50
 EPrint:
 This version is almost identical to the version published electronically on May 10, 2012 in the Canadian Journal of Mathematics