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Tail fields generated by symbol counts in measure-preserving systems

Karl Petersen, Jean-Paul Thouvenot (2004)

Colloquium Mathematicae

A finite-state stationary process is called (one- or two-sided) super-K if its (one- or two-sided) super-tail field-generated by keeping track of (initial or central) symbol counts as well as of arbitrarily remote names-is trivial. We prove that for every process (α,T) which has a direct Bernoulli factor there is a generating partition β whose one-sided super-tail equals the usual one-sided tail of β. Consequently, every K-process with a direct Bernoulli factor has a one-sided super-K generator....

The Geometry of Model Spaces for Probability-Preserving Actions of Sofic Groups

Tim Austin (2016)

Analysis and Geometry in Metric Spaces

Bowen’s notion of sofic entropy is a powerful invariant for classifying probability-preserving actions of sofic groups. It can be defined in terms of the covering numbers of certain metric spaces associated to such an action, the ‘model spaces’. The metric geometry of these model spaces can exhibit various interesting features, some of which provide other invariants of the action. This paper explores an approximate connectedness property of the model spaces, and uses it give a new proof that certain...

The M/M/1 queue is Bernoulli

Michael Keane, Neil O'Connell (2008)

Colloquium Mathematicae

The classical output theorem for the M/M/1 queue, due to Burke (1956), states that the departure process from a stationary M/M/1 queue, in equilibrium, has the same law as the arrivals process, that is, it is a Poisson process. We show that the associated measure-preserving transformation is metrically isomorphic to a two-sided Bernoulli shift. We also discuss some extensions of Burke's theorem where it remains an open problem to determine if, or under what conditions, the analogue of this result...

The $σ$ -algebra of pasts of a random walk on the orbits of the Bernoulli action of the group $ℤ^{d}$ .

Gorbulsky, A.D. (2005)

Zapiski Nauchnykh Seminarov POMI

Théorèmes limites pour une classe de chaînes de Markov et applications aux difféomorphismes d'Anosov

Y. Guivarc'h, J. Hardy (1988)

Annales de l'I.H.P. Probabilités et statistiques

Topics on Meixner families

Marek Bożejko, Nizar Demni (2010)

Banach Center Publications

We shed some light on the inter-connections between different characterizations leading to the classical Meixner family. This allows us to give free analogs of both Sheffer's and Al-Salam and Chihara's characterizations in the classical case by the use of the free derivative operator. The paper closes with a discussion of the q-deformed case, |q| < 1.