Markov operators with a unique invariant measure

Identifying Markov Chains with a Given Invariant Measure

A classification of orbits admitting a unique invariant measure

We consider the space of countable structures with fixed underlying set in a given countable language. We show that the number of ergodic probability measures on this space that are S∞-invariant and concentrated on a single isomorphism class must be zero, or one, or continuum. Further, such an isomorphism class admits a unique S∞-invariant probability measure precisely when the structure is hig...

A non-ergodic probabilistic cellular automaton with a unique invariant measure

We exhibit a Probabilistic Cellular Automaton (PCA) on {0, 1} with a neighborhood of size 2 which is non-ergodic although it has a unique invariant measure. This answers by the negative an old open question on whether uniqueness of the invariant measure implies ergodicity for a PCA.

BOUNDARIES OF INVARIANT MARKOV OPERATORS : THE IDENTIFICATION PROBLEM Vadim

Ergodic Theory of Markov Chains Admitting an Infinite Invariant Measure.