A central object of this book is the discrete Laplace operator on finite and infinite graphs. The eigenvalues of the discrete Laplace operator have long been used in graph theory as a convenient tool for understanding the structure of complex graphs. They can also be used in order to estimate the rate of convergence to equilibrium of a random walk (Markov chain) on finite graphs. For infinite graphs, a study of the heat kernel allows to solve the type problem—a problem of deciding whether the random walk is recurrent or transient. This book starts with elementary properties of the eigenvalues on finite graphs, continues with their estimates and applications, and concludes with heat kernel estimates on infinite graphs and their application to the type problem. The book is suitable for beginners in the subject and accessible to undergraduate and graduate students with a background in linear algebra I and analysis I. It is based on a lecture course taught by the author and includes a wide variety of exercises. The book will help the reader to reach a level of understanding sufficient to start pursuing research in this exciting area.
Simon P. Norton The uniqueness of the Fischer-Griess Monster Edmund F. Robertson Efficiency of finite simple groups and their covering groups Mark A. Ronan Buildings and sporadic groups Stephen D. Smith On the Head characters of the ...
Quan shu zhu yao nei rong bao kuo:qun lun de ji ben gai nian, Zhi huan qun, p qun he mi ling qun, Ke jie qun, Qun zai pei ji he qun shang de zuo yong, Hu su zuo yong he er ci zuo yong, You xian qun de ju bu he zheng ti de dui ying deng.
This book is an introduction to the representation theory of finite groups from an algebraic point of view, regarding representations as modules over the group algebra.
This volume contains papers presented at a conference held in April 2007 at the CRM in Montreal honouring the remarkable contributions of John McKay over four decades of research.
Mathematical Surveys and Monographs
This book is devoted to group-theoretic aspects of topological dynamics such as studying groups using their actions on topological spaces, using group theory to study symbolic dynamics, and other connections between group theory and ...
... Multiple Hilbert Transforms Associated with Polynomials, 2015 R. Bruggeman, J. Lewis, and D. Zagier, Period Functions for Maass Wave Forms and Cohomology, 2015 Chih-Yun Chuang, Ting-Fang Lee, Fu-Tsun Wei, and Jing Yu, Brandt Matrices ...
This volume combines contributions in topology and representation theory that reflect the increasingly vigorous interactions between these areas.