These twenty-six expository papers on random matrices and products of random matrices survey the major results of the last thirty years. They reflect both theoretical and applied concerns in fields as diverse as computer science, probability theory, mathematical physics, and population biology. Many of the articles are tutorial, consisting of examples, sketches of proofs, and interpretations of results. They address a wide audience of mathematicians and scientists who have an elementary knowledge of probability theory and linear algebra, but not necessarily any prior exposure to this specialized area. More advanced articles, aimed at specialists in allied areas, survey current research with references to the original literature. The book's major topics include the computation and behavior under perturbation of Lyapunov exponents and the spectral theory of large random matrices.The applications to mathematical and physical sciences under consideration include computer image generation, card shuffling, and other random walks on groups, Markov chains in random environments, the random Schroedinger equations and random waves in random media. Most of the papers were originally presented at an AMS-IMS-SIAM Joint Summer Research Conference held at Bowdoin College in June, 1984. Of special note are the papers by Kotani on random Schroedinger equations, Yin and Bai on spectra for large random matrices, and Newman on the relations between the Lyapunov and eigenvalue spectra.

Table of Contents:
Limit theorems for products of random matrices by J. C. Watkins Oseledec's multiplicative ergodic theorem by J. Cohen, H. Kesten, and C. M. Newman Products of random matrices: convergence theorems by Y. Guivarch and A. Raugi Examples of application of Oseledec's theorem by F. Ledrappier Multiplicative ergodic theorems for random diffeomorphisms by Y. Kifer Furstenberg-Kesten results: asymptotic anlaysis by S. Pincus Stability of exponential growth rate for randomly perturbed random matrix products via Markov-chain arguments by E. V. Slud Representation, positivity, and expansion of Lyapunov exponents for linear stochastic systems by V. Wihstutz On uniform contraction generated by positive matrices by M. Wojtkowski Lyapunov exponents for some products of random matrices by C. M. Newman A brief survey on the spectral radius and the spectral distribution of large random matrices with i.i.d. entries by V.-R. Hwang Eigenvalues and eigenvectors of large dimensional sample covariance matrices by J. W. Silverstein Spectra for large dimensional random matrices by Y. Q. Yin and Z. D. Bai Products of random matrices and computer image generation by P. Diaconis and M. Shahshahani Products of random matrices as they arise in the study of random walks on groups by P. Diaconis and M. Shahshahani On products of random stochastic matrices by R. Cogburn Convolution sequences of measures on the semigroup of stochastic matrices by M. Rosenblatt Random walks on semigroups by T.-C. Sun A note on random systems with complete connections and their applications to products of random matrices by T. Kaijser Using random matrices to give recurrence and transience criteria for random wlak in a random environment by E. Key A contraction principle for certain Markov chains and its application by G. Letac Lyapunov exponents and spectra for one-dimensional random Schroedinger operators by S. Kotani The density of states of random Schroedinger operators by R. S. Maier Random matrices in nuclear physics and number theory by M. L. Mehta Random matrices and waves in random media by G. Papanicolaou Demographic applications of random matrix products by S. Tuljapurkar.