Translator Disclaimer
May 2021 A nonamenable “factor” of a Euclidean space
Ádám Timár
Author Affiliations +
Ann. Probab. 49(3): 1427-1449 (May 2021). DOI: 10.1214/20-AOP1485

Abstract

Answering a question of Benjamini, we present an isometry-invariant random partition of the Euclidean space Rd, d3, into infinite connected indistinguishable pieces, such that the adjacency graph defined on the pieces is the 3-regular infinite tree. Along the way, it is proved that any finitely generated one-ended amenable Cayley graph can be represented in Rd as an isometry-invariant random partition of Rd to bounded polyhedra, and also as an isometry-invariant random partition of Rd to indistinguishable pieces. A new technique is developed to prove indistinguishability for certain constructions, connecting this notion to factor of IID’s.

Citation

Download Citation

Ádám Timár. "A nonamenable “factor” of a Euclidean space." Ann. Probab. 49 (3) 1427 - 1449, May 2021. https://doi.org/10.1214/20-AOP1485

Information

Received: 1 June 2020; Revised: 1 October 2020; Published: May 2021
First available in Project Euclid: 7 April 2021

Digital Object Identifier: 10.1214/20-AOP1485

Subjects:
Primary: 60D05
Secondary: 20P99

Rights: Copyright © 2021 Institute of Mathematical Statistics

JOURNAL ARTICLE
23 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.49 • No. 3 • May 2021
Back to Top