Entropy of hidden Markov processes and connections to dynamical systems
Subtitle: papers from the Banff International Research Station workshop, October 2007
By: edited by Brian Marcus, Karl Petersen, Tsachy Weissman
Contributors: Banff International Research Station for Mathematics Innovation & Discovery
Series: London Mathematical Society lecture note series -- 385
Publisher: Cambridge University Press
Published: 2011
Place of publication: Cambridge; New York
Language: eng
Number of pages: 272
ISBN-13: 9780521111133
Subjects: Dynamics; Entropy (Information theory); Congresses; Markov processes
Description: "Hidden Markov processes (HMPs) are important objects of study in many areas of pure and applied mathematics, including information theory, probability theory, dynamical systems and statistical physics, with applications in electrical engineering, computer science and molecular biology. This collection of research and survey papers presents important new results and open problems, serving as a unifying gateway for researchers in these areas. Based on talks given at the Banff International Research Station workshop, 2007, this volume addresses a central problem of the subject: computation of the Shannon entropy rate of an HMP. This is a key quantity in statistical physics and information theory, characterising the fundamental limit on compression and closely related to channel capacity, the limit on reliable communication. Also discussed, from a symbolic dynamics and thermodynamical viewpoint, is when mappings between dynamical systems map Markov measures to Markov (or Gibbs) measures or allow for Markov lifts of Markov chains"--
Notes: Includes bibliographical references and index.
Table of contents: title: Machine generated contents note: 1. Hidden Markov processes in the context of symbolic dynamics Mark Boyle and Karl Petersen; 2. On the preservation of Gibbsianess under symbol amalgamation Jean-Rene; Chazottes and E. Ugalde; 3. A note on a complex Hilbert metric with application to domain of analyticity for entropy rate of hidden Markov processes Guangyue Han, Brian Marcus and Yuval Peres; 4. Bounds on the entropy rate of binary hidden Markov processes Erik Ordentlich and Tsachy Weissman; 5. Entropy rate for hidden Markov chains with rare transitions Yuval Peres and Anthony Quas; 6. The capacity of finite-state channels in the high-noise regime Henry Pfister; 7. Computing entropy rates for hidden Markov processes Mark Pollicott; 8. Factors of Gibbs measures for full shifts Mark Pollicott and Thomas Kempton; 9. Thermodynamics of hidden Markov processes Evgeny Verbitskiy.