English

Sofic dimension for discrete measured groupoids

Dynamical Systems 2012-11-13 v2 Group Theory

Abstract

For discrete measured groupoids preserving a probability measure we introduce a notion of sofic dimension that measures the asymptotic growth of the number of sofic approximations on larger and larger finite sets. In the case of groups we give a formula for free products with amalgamation over an amenable subgroup. We also prove a free product formula for measure-preserving actions.

Keywords

Cite

@article{arxiv.1111.2842,
  title  = {Sofic dimension for discrete measured groupoids},
  author = {Ken Dykema and David Kerr and Mikael Pichot},
  journal= {arXiv preprint arXiv:1111.2842},
  year   = {2012}
}

Comments

38 pages, minor changes and corrections

R2 v1 2026-06-21T19:34:56.542Z