Hostname: page-component-7c8c6479df-hgkh8 Total loading time: 0 Render date: 2024-03-28T20:21:29.205Z Has data issue: false hasContentIssue false

Factors of independent and identically distributed processes with non-amenable group actions

Published online by Cambridge University Press:  13 May 2005

KAREN BALL
Affiliation:
Institute for Mathematics and its Applications, University of Minnesota, 400 Lind Hall, 207 Church St. SE, Minneapolis, MN 55455, USA (e-mail: kball@ima.umn.edu) Department of Mathematics, Rawles Hall, Indiana University, Bloomington, IN 47405, USA

Abstract

Let X be a graph and let G be a subgroup of the automorphism group of X. We investigate the question of when the full 2-shift process on the vertices of X has a G-factor process on the same graph consisting of random variables which are independent and identically distributed (i.i.d.) uniform in [0, 1]. We show that such a factor always exists when X is a tree with bounded degrees, no leaves and at least three topological ends, and give a sufficient condition for when such a factor exists if X is a connected graph with infinitely many ends and G acts transitively on the vertices of X. We also show that the full 2m-shift on any finitely-generated non-abelian group G has a G-factor which is i.i.d. uniform on [0, 1] when m is sufficiently large.

Type
Research Article
Copyright
2005 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)