HOROWITZ SEMINAR

PROBABILITY, ERGODIC THEORY and DYNAMICAL SYSTEMS

Omri Sarig (PSU)

will speak on

A necessary & sufficient condition for spectral gap for Ruelle operators on countable Markov shifts

Abstract:

(joint with V. Cyr)
Suppose X is a topologically mixing non compact topological Markov shift, and f:X-->R is locally Holder continuous.
I will describe a necessary & sufficient condition on f for there to exist a "rich" Banach space B=B(f) such that the Ruelle operator of f acts on B with spectral gap.

Application: Suppose X has finite Gurevich entropy, then
the collection of f which admit an equilibrium measure with exponential decay of correlations, CLT, and "no phase transitions" is open and dense for a variety of topologies.

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.