Resolving Markov chains onto Bernoulli shifts
by
Selim Tuncel
University of Washington
Coauthors: Brian Marcus

Results by Boyle and Tuncel and by Ashley, Marcus and Tuncel have shown that measure-preserving versions of right-resolving and right- closing maps settle some basic questions of ergodic theory for Markov chains. Specifically, right-resolving maps characterize one-sided isomorphism, where for both the isomorphism and its inverse the past depends only on the past. More generally, right-closing maps characterize regular isomorphism, where the past is allowed to also use a bounded amount of the future. The problem of finding (simple) necessary and sufficient conditions for the existence of right-closing maps is, thus, brought to the fore. The talk will explain new joint work with Brian Marcus which, for an arbitrary Markov chain and a Bernoulli shift, uses only the basic invariants (\beta, \Delta, c \Delta and periodic points) and an eigenvector for the Markov chain to answer the following questions.

1. Does the Markov chain eventually factor onto the Bernoulli shift by right-closing maps?
2. Does the Markov chain factor onto the Bernoulli shift by a right-closing map?
3. Is the Markov chain regularly isomorphic to the Bernoulli shift?

Date received: March 11, 1998