Information theory for random dynamics

Datum

12.06.2013

Zeit

17:00 - 18:00

Sprecher

Prof. Dr. Tomasz Downarowicz

Zugehörigkeit

Wroclaw University of Technology, Institute of Mathematics and Computer Science

Serie

TUD Dresdner Mathematisches Seminar

Sprache

en

Hauptthema

Mathematik

Andere Themen

Mathematik

Host

Dr. T. Oertel-Jäger

Beschreibung

By "random dynamics" we will mean the action of a Markov (also called doubly stochstic) operator, which is a straightforward generalization of a measure-preserving transformation. In a classical dynamical system a point goes to a point. Here a point goes to a probability distribution (so called transition probability). Although entropy of such "actions" has been defined long ago and in many ways (and all these ways were later shown to give the same resulting entropy value), this was done without any notion of information function. So the "information theory for Markov operators" practically did not exist. For instance, there was no analog of the Shannon-McMillan-Breiman theorem. There are new developments in this direction obtained recently by Bartek Frej and Paulina Frej. In my talk I will speak just about that: I will describe how information function is defined for Markov operators and I will state the analog of the Shannon-McMillan theorem.

Links

• Dresdner Mathematisches Seminar
• Prof. Dr. Tomasz Downarowicz

Letztmalig verändert: 13.03.2013, 14:01:03