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Probability in Banach Spaces
Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.
The Concentration of Measure Phenomenon
The observation of the concentration of measure phenomenon is inspired by isoperimetric inequalities. This book offers the basic techniques and examples of the concentration of measure phenomenon. It presents concentration functions and inequalities, isoperimetric and functional examples, spectrum and topological applications and product measures.
Analysis and Geometry of Markov Diffusion Operators
The present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators. It focuses on the geometric curvature properties of the underlying structure in order to study convergence to equilibrium, spectral bounds, functional inequalities such as Poincaré, Sobolev or logarithmic Sobolev inequalities, and various bounds on solutions of evolution equations. At the same time, it covers a large class of evolution and partial differential equations. The book is intended to serve as an introduction to the subject and to be accessible for beginning and advanced scientists and non-specialists. Simultaneously, it covers a wide range of results and techniques from the early developments in the mid-eighties to the latest achievements. As such, students and researchers interested in the modern aspects of Markov diffusion operators and semigroups and their connections to analytic functional inequalities, probabilistic convergence to equilibrium and geometric curvature will find it especially useful. Selected chapters can also be used for advanced courses on the topic.
The Arts Therapies
The Arts Therapies provides, in one volume, a guide to the different disciplines and their current practice and thinking. It presents: * A clear analysis of the relationship between client, therapist and art form. * An exploration of research, practice and key contributions made to the field by practitioners internationally and within many different contexts. * Discussion of how the arts therapies relate to established health services. The Arts Therapies: A revolution in healthcare is a unique book that provides a thorough and up-to-date overview of the arts therapies. It will prove invaluable to arts therapists, health professionals, and all those who wish to learn more about the field.
Markov Semigroups at Saint-Flour
Bakry, Dominique: Hypercontractivity and its Usage in Semigroup Theory.- Ledoux, Michel: Isoperimetry and Gaussian Analysis.- Saloff-Coste, Laurent: Lectures on Finite Markov Chains.
Mad Dog
The true story of one of pro wrestlingÕs most charismatic, feared, and beloved icons Who was Maurice the man, and who was Mad Dog the character? Maurice ÒMad DogÓ Vachon was a gold medalist, a pro-wrestling legend, and a pop culture icon Ñ but he was also a son, husband, and father. Mad Dog explores VachonÕs career and personal struggles with painstakingly detailed historical research and through both MauriceÕs own recollections and those of the people who knew him best. As a young man, Maurice could have chosen a dark criminal path, but then wrestling and family changed him. Chronicling his slow but steady rise to prominence across America and internationally in some of pro wrestlingÕs most important territories, this in-depth biography shows how VachonÕs life came to be defined by the words of Mark Twain: ÒItÕs not the size of the dog in the fight, itÕs the size of the fight in the dog.Ó Fiercely proud, motivated, and supremely talented, VachonÕs story is also the amazing tale of how a lifelong make-believe heel became a real-life hero outside of the ring. With a foreword by his brother, Paul Vachon, and an afterword by his widow, Kathie Vachon.
The Law of Kinship
In France as elsewhere in recent years, legislative debates over single-parent households, same-sex unions, new reproductive technologies, transsexuality, and other challenges to long-held assumptions about the structure of family and kinship relations have been deeply divisive. What strikes many as uniquely French, however, is the extent to which many of these discussions—whether in legislative chambers, courtrooms, or the mass media—have been conducted in the frequently abstract vocabularies of anthropology and psychoanalysis. In this highly original book, Camille Robcis seeks to explain why and how academic discourses on kinship have intersected and overlapped with political debates o...
Concentration Inequalities
Describes the interplay between the probabilistic structure (independence) and a variety of tools ranging from functional inequalities to transportation arguments to information theory. Applications to the study of empirical processes, random projections, random matrix theory, and threshold phenomena are also presented.
High-Dimensional Probability
High-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions. Drawing on ideas from probability, analysis, and geometry, it lends itself to applications in mathematics, statistics, theoretical computer science, signal processing, optimization, and more. It is the first to integrate theory, key tools, and modern applications of high-dimensional probability. Concentration inequalities form the core, and it covers both classical results such as Hoeffding's and Chernoff's inequalities and modern developments such as the matrix Bernstein's inequality. It then introduces the powerful methods based on stochastic processes, including such tools as Slepian's, Sudakov's, and Dudley's inequalities, as well as generic chaining and bounds based on VC dimension. A broad range of illustrations is embedded throughout, including classical and modern results for covariance estimation, clustering, networks, semidefinite programming, coding, dimension reduction, matrix completion, machine learning, compressed sensing, and sparse regression.
The Random Matrix Theory of the Classical Compact Groups
Provides a comprehensive introduction to the theory of random orthogonal, unitary, and symplectic matrices.
