RANDOM MATRIX THEORY AND ITS APPLICATIONS. MULTIVARIATE STATISTICS AND WIRELESS COMMUNICATIONS

The Institute for Mathematical Sciences at the National University of
Singapore was established on 1 July 2000. Its mission is to foster mathemat-
ical research, both fundamental and multidisciplinary, particularly research
that links mathematics to other disciplines, to nurture the growth of mathe-
matical expertise among research scientists, to train talent for research in
the mathematical sciences, and to serve as a platform for research inter-
action between the scientic community in Singapore and the wider inter-
national community.
The Institute organizes thematic programs which last from one month
to six months. The theme or themes of a program will generally be of
a multidisciplinary nature, chosen from areas at the forefront of current
research in the mathematical sciences and their applications.
Generally, for each program there will be tutorial lectures followed by
workshops at research level. Notes on these lectures are usually made avail-
able to the participants for their immediate benet during the program. The
main objective of the Institute's Lecture Notes Series is to bring these lec-
tures to a wider audience. Occasionally, the Series may also include the pro-
ceedings of workshops and expository lectures organized by the Institute.
The World Scientic Publishing Company has kindly agreed to publish
the Lecture Notes Series. This Volume, \Random Matrix Theory and Its
Applications: Multivariate Statistics and Wireless Communications", is the
eighteenth of this Series. We hope that through the regular publication
of these lecture notes the Institute will achieve, in part, its objective of
promoting research in the mathematical sciences and their applications.

Random matrix theory has a long history, beginning in the first instance in multivariate statistics. It was used by Wigner to supply explanations for the important regularity features of the apparently random dispositions of the energy levels of heavy nuclei. The subject was further deeply developed under the important leadership of Dyson, Gaudin and Mehta, and other mathematical physicists.

In the early 1990s, random matrix theory witnessed applications in string theory and deep connections with operator theory, and the integrable systems were established by Tracy and Widom. More recently, the subject has seen applications in such diverse areas as large dimensional data analysis and wireless communications.

This volume contains chapters written by the leading participants in the field which will serve as a valuable introduction into this very exciting area of research.