Sofic dimension for discrete measured groupoids

Details Sofic dimension for discrete measured groupoids Sofic dimension for discrete measured groupoids

2011-11-11

arxiv.org/abs/1111.2842v1

Mathematics

Dynamical Systems

38 pages

Scientific paper

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.

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