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STOR Colloquium: Terry Soo, University of Kansas
March 19, 2018 @ 3:30 pm - 4:30 pm
The Department of
Statistics and Operations Research
The University of North Carolina at Chapel Hill
Monday, March 19th, 2018
120 Hanes Hall
University of Kansas
ISOMORPHISMS IN PROBABILITY AND ERGODIC THEORY
Two measure-preserving systems are isomorphic if there exists a measure-preserving bijection between them that respects the dynamics of the systems. Kolmogorov (1958) showed that Shannon entropy is an isomorphism invariant for independent and identically distributed systems, and Ornstein (1970) showed it is in fact a complete invariant. A simpler proof of Ornstein’s result for i.i.d. systems was given by Keane and Smorodinsky (1979).
As part of a general theory for the isomorphism problem for actions of an amenable group, Ornstein and Weiss (1987) proved that two Poisson point processes are isomorphic. I will discuss ongoing work with Amanda Wilkens, where we give an elementary proof of the result of Ornstein and Weiss. I will also discuss other probabilistic variants of Ornstein theory.
Refreshments will be served at 3:00pm in the 3rd floor lounge of Hanes Hall