Line up a deck of 52 cards on a table. Randomly choose two cards and switch them. How many switches are needed in order to mix up the deck? Starting from a few concrete problems such as random walks on the discrete circle and the finite ultrametric space this book develops the necessary tools for the asymptotic analysis of these processes. This detailed study culminates with the case-by-case analysis of the cut-off phenomenon discovered by Persi Diaconis. This self-contained text is ideal for graduate students and researchers working in the areas of representation theory, group theory, harmonic analysis and Markov chains. Its topics range from the basic theory needed for students new to this area, to advanced topics such as the theory of Green's algebras, the complete analysis of the random matchings, and the representation theory of the symmetric group.
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(228mm x 152mm x 25mm)
Cambridge University Press
Publisher: Cambridge University Press
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Author Biography - Tullio Ceccherini-Silberstein
Tullio Ceccherini-Silberstein is Professor of Mathematical Analysis in the Department of Engineering at the Universit... del Sannio, Benevento. Fabio Scarabotti is Professor of Mathematical Analysis in the Department of Mathematics at the Universit... degli Studi di Roma 'La Sapienza'. Filippo Tolli is Assistant Professor of Mathematical Analysis in the Department of Mathematics at the Universit... Roma Tre.