From: "Louis M. Pecora" Subject: Re: References for Random Matrix eigenvalue formulas ? Date: Wed, 18 Oct 2000 10:55:48 GMT Newsgroups: sci.physics.research,sci.math.research,sci.math.num-analysis Summary: [missing] In article , Sam wrote: > It is very surprising but a book on programming may help it is called > 'Numerical Recipes' several versions are available - I have the FORTRAN one > which shows my age - ISBN 0521383307 or library of Congress qa297.n866 1989 > 519.4'0285'5369 89-22181 it helped me when I was working on this in > statistical physics of nucleation > > [Moderator's note: While Fortran is the oldest high-level programming > language, modern Fortran---very compatible with older Fortran---is > quite, ah, modern; Fortran95 is the current standard, with the next one > planned for 2002 or so. Fortran is very much alive in very many physics > applications (and elsewhere) and remains the best language for such > tasks. -P.H.] Sam, Thanks, but I have Numerical Recipes and there's nothing on Random Matrices. It's a bit more difficult problem than NR would address, although, generally, the book is great for standard stuff. I have found some references, both here and elsewhere and share them with you all. I have not checked many out, yet. Some sources: http://www.mathsoft.com/asolve/constant/glshkn/gue.html E. L. Basor, C. A. Tracy and H. Widom, Asymptotics of level-spacing distributions for random matrices, Phys. Rev. Lett. 69 (1992) 5-8 and 69 (1992) 2880; MR 93g:82004a and b. Some material on random matrices in Modern Graph Theory by Bollobas. Trust me--- you'll love this book! This is one of my all time favorite books, and I learned alot of fabulous stuff from it :-) Hakim (sp?) papers recommended for regular mtx + rand. Mtx. http://www-math.mit.edu/~edelman/comprehensive.html e.g The Probability that a Random Real Gaussian Matrix Has k Real Eigenvalues, Related Distributions, and the Circular Law by A. Edelman, Journal of Multivariate Analysis 60, (1997), 203--232. Dyson, F. J.. A Brownian-motion model for the eigenvalues of a random matrix, J. Math. Phys. 3}(1962), 1191--1198. Dyson's method generalizes to the other classical Lie algebras, which include skew-symmetric real matrices; I have worked on this, and can send you a reprint of my paper if you can understand the Lie theory.