Tree and grid factors for general point processes

Ádám Timár*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


We study isomorphism invariant point processes of Rd 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 Zn. This perhaps surprising result (that any d and n works) solves a problem by Steve Evans. The construction, based on a connected clumping with 2i vertices in each clump of the i’th partition, can be used to define various other factors.

Original languageEnglish
Pages (from-to)53-59
Number of pages7
JournalElectronic Communications in Probability
Publication statusPublished - 1 Jan 2004

Other keywords

  • Factors
  • Point processes
  • Random grid
  • Random tree


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