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

Published online by Cambridge University Press:  13 May 2005

KAREN BALL
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: [email protected]) Department of Mathematics, Rawles Hall, Indiana University, Bloomington, IN 47405, USA
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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
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 3 , June 2005 , pp. 711 - 730
Copyright
2005 Cambridge University Press

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