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2004 Tree and Grid factors of General Point processes
Adam Timar
Author Affiliations +
Electron. Commun. Probab. 9: 53-59 (2004). DOI: 10.1214/ECP.v9-1073


We study isomorphism invariant point processes of $R^d$ whose groups of symmetries are almost surely trivial. We define a 1-ended, locally finite tree factor on the points of the process, that is, a mapping of the point configuration to a graph on it that is measurable and equivariant with the point process. This answers a question of Holroyd and Peres. The tree will be used to construct a factor isomorphic to $Z^n$. This perhaps surprising result (that any $d$ and $n$ works) solves a problem by Steve Evans. The construction, based on a connected clumping with $2^i$ vertices in each clump of the $i$'th partition, can be used to define various other factors.


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Adam Timar. "Tree and Grid factors of General Point processes." Electron. Commun. Probab. 9 53 - 59, 2004.


Accepted: 21 April 2004; Published: 2004
First available in Project Euclid: 26 May 2016

zbMATH: 1060.60050
MathSciNet: MR2081459
Digital Object Identifier: 10.1214/ECP.v9-1073

Primary: 60G55
Secondary: 60K35


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