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Réimpression inchangée de l'édition originale de 1876.
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.
Covering prehistoric times to the modern era, this fascinating resource presents pro-and-con arguments regarding unresolved, historic controversies throughout the development of the world. Popular Controversies in World History: Investigating History's Intriguing Questions offers uniquely compelling and educational examinations of pivotal events and puzzling phenomena, from the earliest evidence of human activity to controversial events of the 20th century. From the geographic location of human origins, to the authenticity of the Shroud of Turin, to the innocence—or guilt—of Sacco and Vanzetti, Popular Controversies in World History: Investigating History's Intriguing Questions provides four volumes on the ongoing debates that have captivated both the historical community and the public at large. In each chapter, established experts offer credible opposing arguments pertaining to specific debates, providing readers with resources for independent critical thinking on the issue. This format allows students, scholars, and other interested readers to actively engage in some of the most intriguing conundrums facing historians today.
Bulletin des lois, 2e partie. Ordonnances, 1e et 2e section
Includes its Report, 1896-19 .