The Annals of Probability

Finitary isomorphisms of Poisson point processes

Terry Soo and Amanda Wilkens

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Abstract

As part of a general theory for the isomorphism problem for actions of amenable groups, Ornstein and Weiss (J. Anal. Math. 48 (1987) 1–141) proved that any two Poisson point processes are isomorphic as measure-preserving actions. We give an elementary construction of an isomorphism between Poisson point processes that is finitary.

Article information

Source
Ann. Probab., Volume 47, Number 5 (2019), 3055-3081.

Dates
Received: May 2018
Revised: December 2018
First available in Project Euclid: 22 October 2019

Permanent link to this document
https://projecteuclid.org/euclid.aop/1571731444

Digital Object Identifier
doi:10.1214/18-AOP1332

Mathematical Reviews number (MathSciNet)
MR4021244

Subjects
Primary: 37A35: Entropy and other invariants, isomorphism, classification 60G10: Stationary processes 60G55: Point processes

Keywords
Poisson point process finitary isomorphisms

Citation

Soo, Terry; Wilkens, Amanda. Finitary isomorphisms of Poisson point processes. Ann. Probab. 47 (2019), no. 5, 3055--3081. doi:10.1214/18-AOP1332. https://projecteuclid.org/euclid.aop/1571731444


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References

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