Entropy for random group actions

Entropy for random group actions

We consider the entropy of systems of random transformations, where the transformations are chosen from the set of generators of a Z action. We show that the classical definition gives unsatisfactory entropy results in the higher-dimensional case, i.e. when d ≥ 2. We propose a new definition of the entropy for random group actions which agrees with the classical definition in the one-dimensiona...

Entropy for random group actionsRobert

Entropy and mixing for amenable group actions

For Γ a countable amenable group consider those actions of Γ as measurepreserving transformations of a standard probability space, written as {Tγ}γ∈Γ acting on (X,F , μ). We say {Tγ}γ∈Γ has completely positive entropy (or simply cpe for short) if for any finite and nontrivial partition P of X the entropy h(T, P ) is not zero. Our goal is to demonstrate what is well known for actions of Z and ev...

The Erwin Schrr Odinger International Institute for Mathematical Physics Entropy for Random Group Actions

The Abramov–rokhlin Entropy Addition Formula for Amenable Group Actions

In this note we show that the entropy of a skew product action of a countable amenable group satisfies the classical formula of Abramov and Rokhlin.