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Resolving Markov chains onto Bernoulli shifts via positive polynomials

About this Title

Brian Marcus and Selim Tuncel

Publication: Memoirs of the American Mathematical Society
Publication Year: 2001; Volume 150, Number 710
ISBNs: 978-0-8218-2646-1 (print); 978-1-4704-0303-4 (online)
DOI: https://doi.org/10.1090/memo/0710
MathSciNet review: 1810042
MSC: Primary 37A35; Secondary 28D20

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Table of Contents

Chapters

  • A. Resolving Markov chains onto Bernoulli shifts
  • 1. Introduction
  • 2. Weighted graphs and polynomial matrices
  • 3. The main results
  • 4. Markov chains and regular isomorphism
  • 5. Necessity of the conditions
  • 6. Totally conforming eigenvectors and the one-variable case
  • 7. Splitting the conforming eigenvector in the one-variable case
  • 8. Totally conforming eigenvectors for the general case
  • 9. Splitting the conforming eigenvector in the general case
  • B. On large powers of positive polynomials in several variables
  • 1. Introduction
  • 2. Structure of $\operatorname {Log}(p^n)$
  • 3. Entropy and equilibrium distributions for $w\in W(p)$
  • 4. Equilibrium distributions and coefficients of $p^n$
  • 5. Proofs of the estimates