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Group actions and singular martingales

Published online by Cambridge University Press:  16 January 2003

JOSEPH ROSENBLATT ,
DANIEL STROOCK  and
MICHAEL TAYLOR
JOSEPH ROSENBLATT
Affiliation:
Mathematics Department, University of Illinois at Urbana-Champaign, IL 43210, USA (e-mail: jrsnbltt@math.uiuc.edu)
DANIEL STROOCK
Affiliation:
Mathematics Department, Massachusetts Institute of Technology, MA 02139, USA (e-mail: dws@math.mit.edu)
MICHAEL TAYLOR
Affiliation:
Mathematics Department, University of North Carolina at Chapel Hill, NC 27599, USA (e-mail: met@math.unc.edu)
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Abstract

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We investigate properties of a class of martingales formed by picking a measurable set A in a compact group G, taking random rotates of A, and taking measures of the resulting intersections, suitably normalized. Such martingales are shown to yield measures on G^\infty that are singular with respect to product Haar measure, and their ergodic decompositions with respect to the shift map are analyzed. Connections are made with De Finetti theory.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 1 , February 2003 , pp. 293 - 305
Copyright
2003 Cambridge University Press