Products of Random Matrices with Applications to Schrodinger Operators (Progress in Probability) - ISBN:0817633243

Products of Random Matrices with Applications to Schrodinger Operators (Progress in Probability)

Date: 04 June 2011, 05:06

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This book presents two closely related series of lectures.
Part A, due to P. Bougerol, is an introduction to the works of Furstenberg, Guivarc'h, Le Page and Raugi on products of random matrices. Only invertible independent identically distributed random matrices satisfying an irreducibility condition are considered. The purpose is to prove in detail the analogues of the classical limit theorem (e.g. law of large numbers, central limit theorem). This part is based on a course given at the University of Paris 7 in 1983.
Part B, due to J. Lacroix, deals with the spectral theory of random Schrodinger operators, where the products of random matrices play a crucial role. It presents a rigorous and unified treatment of the main known results in the one-dimensional discrete case. Since we are aware that some readers are mainly interested in Schrodinger operators, any notion or result needed from part A is clearly restated (but of course not proved again !).

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