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# Random Matrices and Their Applications

### About this Title

**Joel E. Cohen**, **Harry Kesten** and **Charles M. Newman**, Editors

Publication: Contemporary Mathematics

Publication Year:
1986; Volume 50

ISBNs: 978-0-8218-5044-2 (print); 978-0-8218-7635-0 (online)

DOI: https://doi.org/10.1090/conm/050

MathSciNet review: 841077

### Table of Contents

**Download chapters as PDF**

**Front/Back Matter**

** I. Basic theory of products of random matrices **

- Joseph C. Watkins – Limit theorems for products of random matrices: a comparison of two points of view [MR 841078]
- Joel E. Cohen, Harry Kesten and Charles M. Newman – Oseledec’s multiplicative ergodic theorem: a proof [MR 841079]
- Y. Guivarc’h and A. Raugi – Products of random matrices: convergence theorems [MR 841080]
- F. Ledrappier – Examples of applications of Oseledec’s theorem [MR 841081]

- Yuri Kifer – Multiplicative ergodic theorems for random diffeomorphisms [MR 841082]
- Steve Pincus – Furstenberg-Kesten results: asymptotic analysis [MR 841083]
- Eric V. Slud – Stability of exponential growth rate for randomly perturbed random matrix products via Markov-chain arguments [MR 841084]
- Volker Wihstutz – Representation, positivity and expansion of Lyapunov exponents for linear stochastic systems [MR 841085]

- Maciej Wojtkowski – On uniform contraction generated by positive matrices [MR 841086]

** D. Connections with spectral theory **

- C. M. Newman – Lyapunov exponents for some products of random matrices: exact expressions and asymptotic distributions [MR 841087]

** II. Spectral theory of random matrices **

- Chii-Ruey Hwang – A brief survey on the spectral radius and the spectral distribution of large random matrices with i.i.d. entries [MR 841088]
- Jack W. Silverstein – Eigenvalues and eigenvectors of large-dimensional sample covariance matrices [MR 841089]
- Y. Q. Yin and Z. D. Bai – Spectra for large-dimensional random matrices [MR 841090]

** III. Applications to computer science, probability and statistics of products of random matrices **

** A. Applications to computer science and statistics **

- Persi Diaconis and Mehrdad Shahshahani – Products of random matrices and computer image generation [MR 841091]
- Persi Diaconis and Mehrdad Shahshahani – Products of random matrices as they arise in the study of random walks on groups [MR 841092]

** B. Applications to Markov chains in random environments **

- Robert Cogburn – On products of random stochastic matrices [MR 841093]
- M. Rosenblatt – Convolution sequences of measures on the semigroup of stochastic matrices [MR 841094]
- Tze Chien Sun – Random walks on semigroups [MR 841095]

** Other appliations to probability theory **

- Thomas Kaijser – A note on random systems with complete connections and their applications to products of random matrices [MR 841096]
- Eric S. Key – Using random matrices to give recurrence and transience criteria for random walk in a random environment [MR 841097]
- Gérard Letac – A contraction principle for certain Markov chains and its applications [MR 841098]

** IV. Scientific applications of random matrices and their products **

- S. Kotani – Lyapunov exponents and spectra for one-dimensional random Schrödinger operators [MR 841099]
- Robert S. Maier – The density of states of random Schroedinger operators [MR 841100]
- M. L. Mehta – Random matrices in nuclear physics and number theory [MR 841101]
- George C. Papanicolaou – Random matrices and waves in random media [MR 841102]
- Shripad Tuljapurkar – Demographic applications of random matrix products [MR 841103]

- Joel E. Cohen, Harry Kesten and Charles M. Newman – Open problems [MR 841104]
- Joel E. Cohen – Products of random matrices and related topics in mathematics and science: a bibliography [MR 841105]