Mike Hochman (Hebrew U.)

will speak

An upcrossing inequality for the Shannon-McMillan-Breiman theorem.

Abstract:

I'll describe an upcrossing inequality for the SMB theorem. The exact statement is: For a finite-valued stationary process $(X_n)$ let \[ Y_n = \frac{1}{n} \log P(X_1 X_2 \ldots X_n) \] Then for any nonempty segment $[a,b]$, the probability that the sequence $Y_1 ,Y_2 , ...$ crosses $[a,b]$ more than $L$ times decays exponentially in $L$ at a rate depending only on the segment $[a,b]$, but not on the process $X$. The result holds also for more general group actions. I will give an outline of the proof.

To suggest a talk (yours, or someone elses), contact Jon. Aaronson:

Back to: Jon Aaronson's homepage.

Last update on 20/10/02.