Sofic dimension for discrete measured groupoids

Dykema, Ken; Kerr, David; Pichot, Mikaël

doi:10.1090/S0002-9947-2013-05987-9

Sofic dimension for discrete measured groupoids
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by Ken Dykema, David Kerr and Mikaël Pichot PDF

Trans. Amer. Math. Soc. 366 (2014), 707-748 Request permission

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.

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