Sofic approximations and quantitative measure couplings
arXiv:2205.12137 · doi:10.1215/00192082-11996711
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