@article{ECP1073,
author = {Adam Timar},
title = {Tree and Grid factors of General Point processes},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {9},
year = {2004},
keywords = {Point Processes; factors; random tree; random grid},
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.},
pages = {no. 6, 53-59},
issn = {1083-589X},
doi = {10.1214/ECP.v9-1073},
url = {http://ecp.ejpecp.org/article/view/1073}}