Probability Measures on Semigroups: Convolution Products, Random Walks and Random Matrices

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Springer Science & Business Media, Nov 2, 2010 - Mathematics - 430 pages
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This second edition presents up-to-date material on the theory of weak convergance of convolution products of probability measures in semigroups, the theory of random walks on semigroups, and their applications to products of random matrices. In addition, this unique work examines the essentials of abstract semigroup theory and its application to concrete semigroups of matrices. This substantially revised text includes exercises at various levels at the end of each section and includes the best available proofs on the most important theorems used in a book, making it suitable for a one semester course on semigroups. In addition, it could also be used as a main text or supplementary material for courses focusing on probability on algebraic structures or weak convergance. This book is ideally suited to graduate students in mathematics, and students in other fields, such as engineering and the sciences with an interest in probability. Students in statistics using advanced probability will also find this book useful.

 

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Contents

Chapter 1 Semigroups
1
Chapter 2 Probability Measures on Topological Semigroups
63
Chapter 3 Random Walks on Semigroups
171
Chapter 4 Random Matrices
252
Their Skeletons and Convergence in Distribution
359
Appendix B An Example Due to Chamayou and Letac
365
Appendix C Asymptotic Behavior of 026B30D XnXn1lettoken X0u026B30D for IID Random Nonnegative Matrices
369
Appendix D Continuous Singularity of the Limit Distribution of Products of IID Stochastic Matrices
383
Appendix E Rate of Decay of Concentration Functions on Discrete Groups by TM Retzlaff
397
References
413
Index
423
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