Sofic entropy and measures on model spaces

Sofic entropy and measures on model spaces

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Tim Austin , Courant Institute of Mathematical Sciences
Fine Hall 401

Please note special day (Friday) and location (Fine 401).  Sofic entropy is an invariant for probability-preserving actions of sofic groups introduced a few years ago by Lewis Bowen. It generalizes some parts of classical Kolmogorov-Sinai entropy theory to actions of such groups. But in other respects it behaves less regularly than Kolmogorov-Sinai entropy.  After giving a short introduction to sofic entropy, I will discuss conditions under which it is additive under Cartesian products. It is always subadditive, but the reverse inequality can fail. However, there is a general lower bound in terms of separate quantities for the two factor systems involved. One of these quantities is a variant of sofic entropy, defined using probability distributions on the spaces of good models of an action rather than individual good models. This lower bound turns out to be optimal in a certain sense, and it can be used to derive some sufficient conditions for the strict additivity of sofic entropy itself.