PREFACE
The purpose of this volume is to describe some recent and not so recent
discoveries about random matrices and their applications to a wide audience of
scientists and pure and applied mathematicians. The authors were requested to
provide exposition, not detailed reports of new research; to give simple,
concrete and vivid examples of significant phenomena, rather than abstract but
inaccessible theorems that might cover all possibilities. The papers provide
heuristic interpretations of results, sketch the ideas of proofs, and point to
or comment on the original reports of research. The papers draw on or
describe applications in the fields of probability theory, functional
analysis, group theory, mathematical physics, statistics, computer science,
population biology, and number theory. All papers were refereed for
expository and technical quality. The editors are grateful for the
co-operative efforts of the authors and the referees.
The papers in this volume fall into two broad groups: those concerned
with products of random matrices and those in which the multiplication of
random matrices plays no role. Interest in random matrices per se has a
fairly long tradition in statistics and in physics (e.g. Mehta, 1967)
[citations are given in the bibliography at the end of the book). Interest in
products of random matrices can be dated from the first published paper on the
topic by Bellman (1956). The results about the asymptotic behavior of
products of random matrices discovered by Furstenberg and Kesten (1960) led to
much of the interest in products of random matrices over the last twenty-five
years, as many of the papers on products of random matrices in this volume
demonstrate.
Most of these papers were presented at a meeting on random matrices and
their applications, organized as an AMS-IMS-SIAM Joint Summer Research
Conference in the Mathematical Sciences at Bowdoin College, Brunswick, Maine,
17-23 June 1984. This may have been the first, but was certainly not the
only, conference devoted to random matrices and their applications.
Simultaneously with the Bowdoin meeting, a meeting on products of random
matrices was held in Toulouse, France. In November 1984 another meeting on
Lyapounov exponents was held in Bremen, West Germany.
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