Vol. 294, No. 1, 2018

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Mixing properties for hom-shifts and the distance between walks on associated graphs

Nishant Chandgotia and Brian Marcus

Vol. 294 (2018), No. 1, 41–69

Let be a finite connected undirected graph and  walk2 be the graph of bi-infinite walks on ; two such walks {xi}i and {yi}i are said to be adjacent if xi is adjacent to yi for all i . We consider the question: Given a graph , when is the diameter (with respect to the graph metric) of  walk2 finite? Such questions arise while studying mixing properties of hom-shifts (shift spaces which arise as the space of graph homomorphisms from the Cayley graph of d with respect to the standard generators to ) and are the subject of this paper.

walks on graphs, folding, block-gluing, symbolic dynamics, strong irreducibility, universal covers
Mathematical Subject Classification 2010
Primary: 37B10
Secondary: 68R10, 82B20
Received: 5 October 2016
Revised: 28 May 2017
Accepted: 19 October 2017
Published: 5 January 2018
Nishant Chandgotia
School of Mathematical Sciences
Tel Aviv University
Tel Aviv
Brian Marcus
Department of Mathematics
University of British Columbia
Vancouver, BC