## 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.## References

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## Additional Information

**Ken Dykema**- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
- MR Author ID: 332369
- Email: kdykema@math.tamu.edu
**David Kerr**- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
- MR Author ID: 361613
- Email: kerr@math.tamu.edu
**Mikaël Pichot**- Affiliation: Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada H3A 2K6
- Email: mikael.pichot@mcgill.ca
- Received by editor(s): March 28, 2012
- Published electronically: September 4, 2013
- Additional Notes: The first author was partially supported by NSF grant DMS-0901220

The second author was partially supported by NSF grant DMS-0900938

The third author was partially supported by JSPS - © Copyright 2013 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**366**(2014), 707-748 - MSC (2010): Primary 20L05, 20E06, 37A15
- DOI: https://doi.org/10.1090/S0002-9947-2013-05987-9
- MathSciNet review: 3130315