Isomorphic random Bernoulli shifts

How to Find an Extra Head: Optimal Random Shifts of Bernoulli and Poisson Random Fields

Weak isomorphisms between Bernoulli shifts

In this note, we prove that if G is a countable group that contains a nonabelian free subgroup then every pair of nontrivial Bernoulli shifts over G are weakly isomorphic.

Brooks’ theorem for Bernoulli shifts

If Γ is an infinite group with finite symmetric generating set S, we consider the graph G(Γ, S) on [0, 1]Γ by relating two distinct points if an element of s sends one to the other via the shift action. We show that, aside from the cases Γ = Z and Γ = (Z/2Z) ∗ (Z/2Z), G(Γ, S) satisfies a measure-theoretic version of Brooks’ theorem: there is a G(Γ, S)-invariant conull Borel set B ⊆ [0, 1]Γ and ...

Institute for Mathematical Physics Resolving Markov Chains onto Bernoulli Shifts Resolving Markov Chains onto Bernoulli Shifts

Uniform Endomorphisms Which Are Isomorphic to a Bernoulli Shift

A uniformly p to one endomorphism is a measure preserving map with entropy log p which is a.e. p to 1 and for which the conditional expectation of each preimage is precisely 1/p. The standard example of this is one sided p-shift with uniform i.i.d. Bernoulli measure. We give a characterization of those uniformly finite to one endomorphisms conjugate to this standard example by a condition on th...