Random matrices and quantum chaos

  1. Thomas Kriecherbauer*,
  2. Jens Marklof†,‡, and
  3. Alexander Soshnikov§
  1. *Mathematisches Institut, Ludwig-Maximilians-Universität, Theresienstrasse 39, D-80333 Munich, Germany; †School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom; and §Department of Mathematics, University of California, One Shields Avenue, Davis, CA 95616-8633

Abstract

The theory of random matrices has far-reaching applications in many different areas of mathematics and physics. In this note, we briefly describe the state of the theory and two of the perhaps most surprising appearances of random matrices, namely in the theory of quantum chaos and in the theory of prime numbers.

Footnotes

  • ↵ ‡ To whom reprint requests should be addressed. E-mail: j.marklof{at}bristol.ac.uk.

  • This paper is a summary of a session presented at the sixth annual German–American Frontiers of Science symposium, held June 8–10, 2000, at the Arnold and Mabel Beckman Center of the National Academies of Science and Engineering in Irvine, CA.

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  1. PNAS September 11, 2001 vol. 98 no. 19 10531-10532
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