Sofic approximations and quantitative measure couplings

Abstract

We build quantitative measure subgroup couplings from a Brieussel-Zheng diagonal product to a lamplighter group. We use them to answer the inverse problem of the quantification; namely, find a group admitting a measure subgroup coupling with a prescribed group with prescribed quantification, in the case of the lamplighter group.

Updated with comments from the referees. Accepted to publication in Illinois Journal of Mathematics

References in corpus (3)

• Growth of permutational extensions
• Groups of given intermediate word growth
• Building prescribed quantitative orbit equivalence with the group of integers