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Entropy of Hidden Markov Processes and Connections to Dynamical Systems
Papers from the Banff International Research Station Workshop

Part of London Mathematical Society Lecture Note Series

Mark Boyle, Karl Petersen, Jean-René Chazottes, E. Ugalde, Guangyue Han, Brian Marcus, Yuval Peres, Erik Ordentlich, Tsachy Weissman, Anthony Quas, Henry Pfister, Mark Pollicott, Thomas Kempton, Evgeny Verbitskiy
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  • Date Published: May 2011
  • availability: Available
  • format: Paperback
  • isbn: 9780521111133

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About the Authors
  • 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 the problem of characterizing the mappings between dynamical systems which map Markov measures to Markov (or Gibbs) measures, and which allow for Markov lifts of Markov chains.

    • Includes the latest results in an active area of research
    • Connects approaches from various disciplines
    • Discusses open problems such as the computation of the Shannon entropy rate of an HMP
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    Product details

    • Date Published: May 2011
    • format: Paperback
    • isbn: 9780521111133
    • length: 280 pages
    • dimensions: 228 x 152 x 16 mm
    • weight: 0.4kg
    • contains: 8 b/w illus.
    • availability: Available
  • Table of Contents

    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-René 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.

  • Editors

    Brian Marcus, University of British Columbia, Vancouver
    Brian Marcus is a Professor in the Department of Mathematics at the University of British Columbia. He is a Fellow of the IEEE and was co-recipient of the Leonard G. Abraham Prize Paper Award of the IEEE Communications Society in 1993. He has published over 60 research papers and holds 12 US patents.

    Karl Petersen, University of North Carolina, Chapel Hill
    Karl Petersen is a Professor of Mathematics at the University of North Carolina, Chapel Hill. He has previously written the book Ergodic Theory (Cambridge, 1983) and numerous research papers.

    Tsachy Weissman, Stanford University, California
    Tsachy Weissman is an Associate Professor of Electrical Engineering at Stanford University, California and at the Technion. He is a recipient of the joint Information Theory - Communication Society best paper award, a Horev Fellowship for Leaders in Science and Technology and the Henry Taub Prize for excellence in research. He currently serves as Associate Editor of Shannon Theory for the IEEE Transactions on Information Theory.

    Contributors

    Mark Boyle, Karl Petersen, Jean-René Chazottes, E. Ugalde, Guangyue Han, Brian Marcus, Yuval Peres, Erik Ordentlich, Tsachy Weissman, Anthony Quas, Henry Pfister, Mark Pollicott, Thomas Kempton, Evgeny Verbitskiy

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