SOFIC DIMENSION FOR DISCRETE MEASURED GROUPOIDS Academic Article uri icon

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.

published proceedings

  • TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

author list (cited authors)

  • Dykema, K., Kerr, D., & Pichot, M.

citation count

  • 13

complete list of authors

  • Dykema, Ken||Kerr, David||Pichot, Mikael

publication date

  • February 2014