Information theory for random dynamics

Date

Jun 12, 2013

Time

5:00 PM - 6:00 PM

Speaker

Prof. Dr. Tomasz Downarowicz

Affiliation

Wroclaw University of Technology, Institute of Mathematics and Computer Science

Series

TUD Dresdner Mathematisches Seminar

Language

en

Main Topic

Mathematik

Other Topics

Mathematik

Host

Dr. T. Oertel-Jäger

Description

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

Last modified: Mar 13, 2013, 2:01:03 PM