A nonamenable “factor” of a Euclidean space
نویسندگان
چکیده
Answering a question of Benjamini, we present an isometry-invariant random partition the Euclidean space Rd, d≥3, into infinite connected indistinguishable pieces, such that adjacency graph defined on pieces is 3-regular tree. Along way, it proved any finitely generated one-ended amenable Cayley can be represented in Rd as to bounded polyhedra, and also pieces. A new technique developed prove indistinguishability for certain constructions, connecting this notion factor IID’s.
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ژورنال
عنوان ژورنال: Annals of Probability
سال: 2021
ISSN: ['0091-1798', '2168-894X']
DOI: https://doi.org/10.1214/20-aop1485