6 papers · 1 filter
Exploding Markov operators
Bartosz Frej
A special class of doubly stochastic (Markov) operators is constructed. These operators come from measure preserving transformations and inherit some of their properties, namely er…
A comment on ergodic theorem for amenable groups
Bartosz Frej, Dawid Huczek
We prove a version of ergodic theorem for an action of an amenable group, where a Fø lner sequence needs not to be tempered. Instead, it is assumed that a function satisfies certai…
Extensions of Full Shifts with Group Actions
Bartosz Frej, Dawid Huczek
We give a sufficient condition for a symbolic topological dynamical system with action of a countable amenable group to be an extension of the full shift, a problem analogous to th…
Doubly stochastic operators with zero entropy
Bartosz Frej, Dawid Huczek
We study doubly stochastic operators with zero entropy. We generalize three famous theorems: the Rokhlin's theorem on genericity of zero entropy, the Kushnirenko's theorem on equiv…
Faces of simplices of invariant measures for actions of amenable groups
Bartosz Frej, Dawid Huczek
We prove that every face in the simplex of invariant measures on a zero-dimensional dynamical system with free action of an amenable group can be modeled as the entire simplex…
Shearer's inequality and Infimum Rule for Shannon entropy and topological entropy
Tomasz Downarowicz, Bartosz Frej, Pierre-Paul Romagnoli
We review subbadditivity properties of Shannon entropy, in particular, from the Shearer's inequality we derive the "infimum rule" for actions of amenable groups. We briefly discuss…