UW Rainwater Seminar
Winter 2011
Date: January 25 at 2:30
Location: UW
Padelford C-401
Speaker: Karoly Simon, Budapest Technical University
Title: Stationary measures for projective transformations: the Blackwell measure
Abstract:
The Blackwell measure, at least in the particular case of binary symmetric channels, is an invariant measure for
linear fractional transformations with a certain class of rational weights. This measure was introduced by Blackwell in
1957, and it plays a central role in understanding the entropy rate of
fundamental models in information theory (the so-called ``hidden Markov chains''). We show that for a suitable range of
parameter values this measure is necessarily singular. The methods are based on the theory of iterated function systems
with place dependent probabilities.
No prior knowledge of information theory or iterated function systems is assumed; all the necessary definitions and
background will be provided during the talk.
The talk is based on a joint work with B. Barany and M. Pollicott.