Finitary isomorphisms of Poisson point processes

Abstract

As part of a general theory for the isomorphism problem for actions of amenable groups, Ornstein and Weiss (J. Anal. Math. 48:1-141,1987) 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.

arXiv commentPublished version at https://doi.org/10.1214/18-AOP1332 in the Annals of Probability by the Institute of Mathematical Statistics

References in corpus (1)

• Poisson splitting by factors

Cited by in corpus (2)

• Isomorphisms of Poisson systems over locally compact groups
• Finitary isomorphisms of Brownian motions