This book gives a comprehensive and self-contained introduction to the theory of symmetric Markov processes and symmetric quasi-regular Dirichlet forms. In a detailed and accessible manner, Zhen-Qing
Japanese mathematicians Fukushima (Osaka U.), Yoichi Oshima (Kumamato U.), and Masayoshi Takeda (Tohoku U.) begin with an introductory and comprehensive account of the theory of (symmetric) Dirichlet
Revising his unpublished lecture notes, Oshima (U. of Erlangen-Nurnberg) extends results for symmetric Dirichlet forms to lower bounded semi-Dirichlet forms and to time-dependent semi-Dirichlet forms.
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.
