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Block Tridiagonal Matrices and a Beefed-up Version of the Ehrenfest Urn Model

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Book cover Modern Analysis and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 190))

Abstract

The very classical Ehrenfest urn model can be solved exactly in terms of Krawtchouk polynomials. I consider a natural extension of this model which goes beyond “nearest neighbours” random walks and whose analysis benefits from the study of a family of matrix-valued orthogonal polynomials. This subject was started by M.G. Krein around 1949. This paper shows one more example of his vast and lasting legacy in the never-ending task of finding new mathematical tools to analyze the physical world.

The author was supported in part by NSF Grant # DMS 0603901.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley, CA, 94720, USA

    F. Alberto Grünbaum

Authors
  1. F. Alberto Grünbaum
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Editor information

Editors and Affiliations

  1. Department of Theoretical Physics, Odessa National I.I. Mechnikov University, Dvoryanska st. 2, 65026, Odessa, Ukraine

    Vadim M. Adamyan

  2. Department of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Ramat Aviv, Israel

    Israel Gohberg

  3. Institute of Mathematics, Ukrainian National Academy of Sciences, Tereshchenkivska st., 01601, Kyiv-4, Ukraine

    Anatoly Kochubei , Yurij Berezansky , Myroslav Gorbachuk  & Valentyna Gorbachuk , ,  & 

  4. Department of Mathematical Physics, Odessa National I.I. Mechnikov University, Dvoryanska st. 2, 65026, Odessa, Ukraine

    Gennadiy Popov

  5. Institute of Analysis and Scientific Computing, Technical University of Vienna, Wiedner Hauptstrasse 8-10, 1040, Vienna, Austria

    Heinz Langer

Additional information

To the memory of Prof. Mark G. Krein, with gratitude.

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© 2009 Birkhäuser Verlag Basel/Switzerland

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Alberto Grünbaum, F. (2009). Block Tridiagonal Matrices and a Beefed-up Version of the Ehrenfest Urn Model. In: Adamyan, V.M., et al. Modern Analysis and Applications. Operator Theory: Advances and Applications, vol 190. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9919-1_15

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