Local Limit Theorems for Inhomogeneous Markov Chains

​Dmitry Dolgopyat is a Distiguished Professor at the University of Maryland, and a member of the advisory board of the Brin Mathematics Research Center. He obtained his doctorate from Princeton University, and has held positions at the University of California at Berkeley, and at the Pennsylvania State University. Omri Sarig is the Theodore R. and Edlyn Racoosin Professor of Mathematics at the Weizmann Institute of Science. He obtained his doctorate from Tel-Aviv University, and has held positions at the University of Warwick  and the Pennsylvania State University.  ​Dmitry Dolgopyat and Omri Sarig work at the intersection of ergodic theory, probability theory, and the theory of dynamical systems. They have an ongoing collaboration aimed at studying probabilistic limit theorems  for dynamical systems.

• - 1. Overview. - 2. Markov Arrays, Additive Functionals, and Uniform Ellipticity. - 3. Variance Growth, Center-Tightness, and the Central Limit Theorem. - 4. The Essential Range and Irreducibility. - 5. The Local Limit Theorem in the Irreducible Case. - 6. The Local Limit Theorem in the Reducible Case. - 7. Local Limit Theorems for Moderate Deviations and Large Deviations. - 8. Important Examples and Special Cases. - 9. Local Limit Theorems for Markov Chains in Random Environments.