Abstract
A course of lectures was given at the Jawaharlal Nehru University and the Jamia Milia Islamia, New Delhi, during February—March 1996. The following notes were distributed to the audience before each lecture. These notes, which are sketchy and do not go in details, were meant to help students follow the standard literature on the subject. They are collected here (with the exercises!) in the hope that they might prove useful to a larger community of research workers.
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References
M L Mehta,Random matrices (Academic Press, New York, 1991) (referred to as RM in the text)
M L Mehta,Matrix theory (Hindustan Publishing Corporation, Delhi, India) or Les Editions de Physique, Z.I. de Courtaboeuf, B.P. 112, 91944 Les Ulis, France, 1989 (referred to as MT in the text)
“Method of integration over matrix variables: 1–4”,Comm. Math. Phys. 79, 327–340 (1981);Indian J. Pure Appl. Math. 22, 531–546 (1991);J. Phys. A14, 579–586 (1981);J. Phys. 11, 1093–1108 (1991)
M L Mehta and J des Cloizeaux, The probability for several consecutive eigenvalues of a random matrix,Indian J. Pure Appl. Math. 3, 329–351 (1972)
Some papers on Painlevé equations initiated by Jimbo, Miwa, Sato and Ueno of the Kyoto school of mathematics: a good starting point is “Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent” by M Jimbo, T Miwa and Y Mori,Physica D 80–158 (1980). Also the thesis of B Dietz, University of Essen, Germany (1991) and that of A Edelman, Massachusetts Institute of Technology, Cambridge MA, USA are a good reading
K Aomoto, Jacobi polynomials associated with Selberg integrals,SIAM J. Math. Anal. 18, 545–549 (1987)
E P Wigner,Group Theory (Academic Press, New York, 1959)
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Mehta, M.L. Random matrices and matrix models: The JNU lectures. Pramana - J Phys 48, 7–48 (1997). https://doi.org/10.1007/BF02845621
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DOI: https://doi.org/10.1007/BF02845621