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Ultraproducts of measure preserving actions and graph combinatorics

Published online by Cambridge University Press:  16 February 2012

CLINTON T. CONLEY ,
ALEXANDER S. KECHRIS  and
ROBIN D. TUCKER-DROB
CLINTON T. CONLEY
Affiliation:
Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Währinger Strasse 25, 1090 Wien, Austria 584 Malott Hall, Department of Mathematics, Cornell University, Ithaca, NY 14853-4201, USA
ALEXANDER S. KECHRIS
Affiliation:
Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA (email: kechris@caltech.edu)
ROBIN D. TUCKER-DROB
Affiliation:
Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA (email: kechris@caltech.edu)
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Abstract

Ultraproducts of measure preserving actions of countable groups are used to study the graph combinatorics associated with such actions, including chromatic, independence and matching numbers. Applications are also given to the theory of random colorings of Cayley graphs and sofic actions and equivalence relations.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 33 , Issue 2 , April 2013 , pp. 334 - 374
Copyright
©2012 Cambridge University Press

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