Finitary isomorphisms of Poisson point processes

DOI10.1214/18-AOP1332zbMath1447.37015arXiv1805.04600OpenAlexW3101817102MaRDI QIDQ2280549

Amanda Wilkens, Terry Soo

Publication date: 18 December 2019

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.04600

zbMATH Keywords

Poisson point processfinitary isomorphisms

Mathematics Subject Classification ID

Stationary stochastic processes (60G10) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) General groups of measure-preserving transformations and dynamical systems (37A15)

Related Items (5)

Finitary isomorphisms of renewal point processes and continuous-time regenerative processes ⋮ Point processes, cost, and the growth of rank in locally compact groups ⋮ Isomorphisms of Poisson systems over locally compact groups ⋮ Finitary isomorphisms of some infinite entropy Bernoulli flows ⋮ Finitary isomorphisms of Brownian motions

Cites Work

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• The conjugacy problem in ergodic theory
• Poisson splitting by factors
• Entropy and isomorphism theorems for actions of amenable groups
• Notes on geometry
• Explicit codes for some infinite entropy Bernoulli shifts
• A class of finitary codes
• Bernoulli schemes of the same entropy are finitarily isomorphic
• Finitary isomorphisms of some infinite entropy Bernoulli flows
• Bernoulli shifts with the same entropy are isomorphic
• Deterministic thinning of finite Poisson processes
• Newton’s Laws and Coin Tossing
• Universal finitary codes with exponential tails
• The isomorphism problem in ergodic theory

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