Sofic dimension for discrete measured groupoids

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.

38 pages, minor changes and corrections

References in corpus (3)

• Free Entropy Dimension in Amalgamated Free Products
• Orbit equivalence and sofic approximation
• Sofic representations of amenable groups

Cited by in corpus (1)

• Entropy theory for sofic groupoids I: the foundations