Timár, Ádám (2021) A Nonamenable "Factor" of a Euclidean Space. ANNALS OF PROBABILITY, 49 (3). pp. 14271449. ISSN 00911798

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Abstract
Answering a question of Benjamini, we present an isometryinvariant random partition of the Euclidean space Rd, d >= 3, into infinite connected indistinguishable pieces, such that the adjacency graph defined on the pieces is the 3regular infinite tree. Along the way, it is proved that any finitely generated oneended amenable Cayley graph can be represented in Rd as an isometryinvariant random partition of Rd to bounded polyhedra, and also as an isometryinvariant 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.
Item Type:  Article 

Uncontrolled Keywords:  Indistinguishability; Factor of IID; Random tiling; isometryinvariant tiling; 
Subjects:  Q Science / természettudomány > QA Mathematics / matematika 
SWORD Depositor:  MTMT SWORD 
Depositing User:  MTMT SWORD 
Date Deposited:  04 Jan 2022 15:48 
Last Modified:  26 Apr 2023 11:03 
URI:  http://real.mtak.hu/id/eprint/135349 
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