5 citations · 5 across the 3 of their papers we have counts for
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Predictability, topological entropy and invariant random orders
Andrei Alpeev, Tom Meyerovitch, Sieye Ryu
We prove that a topologically predictable action of a countable amenable group has zero topological entropy, as conjectured by Hochman. On route, we investigate invariant random or…
Kolmogorov complexity and entropy of amenable group actions
Andrei Alpeev
It was proved by Brudno that entropy and Kolmogorov complexity for dynamical systems are tightly related. We generalize his results to the case of arbitrary computable amenable gro…
Weak containment and maximal sofic approximations
Andrei Alpeev
We show that the class of sofic actions is closed under direct products and contains a (non-unique) maximal element in the weak containment order. For any sofic group we construct…
Random ordering formula for sofic and Rokhlin entropy of Gibbs measures
Andrei Alpeev
We prove the explicit formula for sofic and Rokhlin entropy of actions arising from some class of Gibbs measures. It provides a new set of examples with sofic entropy independent o…
On Pinsker factors for Rokhlin entropy
Andrei Alpeev
In this paper we will prove that any dynamical system posess the unique maximal factor of zero Rokhlin entropy, so-called Pinsker factor. It is proven also, that if the system is e…