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Finitary isomorphisms of Poisson point processes

Soo, T; Wilkens, A; (2019) Finitary isomorphisms of Poisson point processes. The Annals of Probability , 47 (5) pp. 3055-3081. 10.1214/18-aop1332. Green open access

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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 measurepreserving actions. We give an elementary construction of an isomorphism between Poisson point processes that is finitary.

Type: Article
Title: Finitary isomorphisms of Poisson point processes
Open access status: An open access version is available from UCL Discovery
DOI: 10.1214/18-aop1332
Publisher version: https://doi.org/10.1214/18-aop1332
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Poisson point process, finitary isomorphisms
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10089071
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