HOROWITZ SEMINAR

PROBABILITY, ERGODIC THEORY and DYNAMICAL SYSTEMS

Boris Begun (Hebrew U)

will speak on

Partitions with independent iterates.

Abstract:

(Joint work with A. del Junco)
Consider a measure-preserving transformation of a probability space.

A finite partition of the space is called weakly independent if there are infinitely many images of this partition under powers of the transformation that are jointly independent.
Krengel proved that a transformation is weakly mixing if and only if weakly independent partitions of the underlying space are dense among all finite partitions.
This result has been generalized to actions of discrete amenable groups.

Now consider a random dynamical system (skew product) that is weakly mixing relative to the base.
The independence of partitions can be defined in relation to the base.
Also in this relative setting there exists a counterpart of Krengel's result.

The principal ingredient of the proofs is a result on extension of stationary measures, in other words,
building stationary stochastic processes (with discrete time) from its marginals.
This result is probably interesting in its own right.

To suggest a talk (yours, or someone elses), contact Jon. Aaronson: aaro at post dot tau dot ac dot il

Back to: Jon Aaronson's homepage.

Last update on 12/10/08.