Random Walks on Reductive Groups 1st ed. 2016 Edition

Ebook Details

Authors

Yves Benoist, Jean-François Quint

Year 2016
Pages 323
Publisher Springer
Language en
ISBN 9783319477190
File Size 1.76 MB
File Format PDF
Download Counter 117
Amazon Link

Ebook Description

The classical theory of random walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to products of independent identically distributed random matrices with real coefficients.Under the assumption that the action of the matrices is semisimple – or, equivalently, that the Zariski closure of the group generated by these matrices is reductive - and under suitable moment assumptions, it is shown that the norm of the products of such random matrices satisfies a number of classical probabilistic laws.This book includes necessary background on the theory of reductive algebraic groups, probability theory and operator theory, thereby providing a modern introduction to the topic.