Random Matrices and Their Applications.

Intro -- Contents -- Preface -- I. Basic theory of products of random matrices -- A. Overviews: -- Limit theorems for products of random matrices: a comparison of two points of view -- Oseledec's multiplicative ergodic theorem: a proof -- Products of random matrices: convergence theorems -- Examples of application of Oseledec's theorem -- B. Perturbation theory: -- Multiplicative ergodic theorems for random diffeomorphisms -- Furstenberg-Kesten results: asymptotic analysis -- Stability of exponential growth rate for randomly perturbed random matrix products via Markov-chain arguments -- Representation, positivity and expansion of Lyapunov exponents for linear stochastic systems -- C. Theory of matrix products: -- On uniform contraction generated by positive matrices -- D. Connections with spectral theory: -- Lyapunov exponents for some products of random matrices: exact expressions and asymptotic distributions -- II. Spectral theory of random matrices -- A brief survey on the spectral radius and the spectral distribution of large random matrices with i.i.d. entries -- Eigenvalues and eigenvectors of large dimensional sample covariance matrices -- Spectra for large dimensional random matrices -- III. Applications to computer science, probability and statistics of products of random matrices -- A. Applications to computer science and statistics: -- Products of random matrices and computer image generation -- Products of random matrices as they arise in the study of random walks on groups -- B. Applications to Markov chains in random environments: -- On products of random stochastic matrices -- Convolution sequences of measures on the semigroup of stochastic matrices -- Random walks on semigroups -- C. Other applications to probability theory: -- A note on random systems with complete connections and their applications to products of random matrices.

Using random matrices to give recurrence and transience criteria for random walk in a random environment -- A contraction principle for certain Markov chains and its applications -- IV. Scientific applications of random matrices and their products -- Lyapounov exponents and spectra for one-dimensional random Schroedinger operators -- The density of states of random Schroedinger operators -- Random matrices in nuclear physics and number theory -- Random matrices and waves in random media -- Demographic applications of random matrix products -- V. Supplements -- Open problems -- List of participants in Joint Summer Research Conference at Bowdoin College, 17-23 June 1984 -- Products of random matrices and related topics in mathematics and science: a bibliography.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.