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Tree and Grid factors of General Point processes


 
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1. Title Title of document Tree and Grid factors of General Point processes
 
2. Creator Author's name, affiliation, country Adam Timar; Indiana University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Point Processes; factors; random tree; random grid
 
3. Subject Subject classification 60G55; 60K35
 
4. Description Abstract 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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7. Date (YYYY-MM-DD) 2004-04-21
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1073
 
10. Identifier Digital Object Identifier 10.1214/ECP.v9-1073
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 9
 
12. Language English=en
 
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