Michel Ledoux - Böcker

The observation of the concentration of measure phenomenon is inspired by isoperimetric inequalities. A familiar example is the way the uniform measure on the standard sphere $S^n$ becomes concentrated around the equator as the dimension gets large. This property may be interpreted in terms of functions on the sphere with small oscillations, an idea going back to Levy. The phenomenon also occurs in probability, as a version of the law of large numbers, due to Emil Borel. This book offers the basic techniques and examples of the concentration of measure phenomenon. The concentration of measure phenomenon was put forward in the early seventies by V. Milman in the asymptotic geometry of Banach spaces. It is of powerful interest in applications in various areas, such as geometry, functional analysis and infinite-dimensional integration, discrete mathematics and complexity theory, and probability theory.Particular emphasis is on geometric, functional, and probabilistic tools to reach and describe measure concentration in a number of settings. This book presents concentration functions and inequalities, isoperimetric and functional examples, spectrum and topological applications, product measures, entropic and transportation methods, as well as aspects of M. Talagrand's deep investigation of concentration in product spaces and its application in discrete mathematics and probability theory, supremum of Gaussian and empirical processes, spin glass, random matrices, etc. Prerequisites are a basic background in measure theory, functional analysis, and probability theory.

This book aims to provide an efficient methodology of solving a fluid mechanics problem, based on an awareness of the physical. It meets different objectives of the student, the future engineer or scientist: Simple sizing calculations are required to master today's numerical approach for solving complex practical problems.

Heat is a branch of thermodynamics that occupies a unique position due to its involvement in the field of practice. Being linked to the management, transport and exchange of energy in thermal form, it impacts all aspects of human life and activity. Heat transfers are, by nature, classified as conduction, convection (which inserts conduction into fluid mechanics) and radiation. The importance of these three transfer methods has resulted – justifiably – in a separate volume being afforded to each of them. This first volume is dedicated to thermal conduction, and, importantly, assumes an analytical approach to the problems presented, and recalls the fundamentals. Heat Transfer 1 combines a basic approach with a deeper understanding of the discipline and will therefore appeal to a wide audience, from technician to engineer, from doctoral student to teacher-researcher.

Heat is a branch of thermodynamics that occupies a unique position due to its involvement in the field of practice. Being linked to the management, transport and exchange of energy in thermal form, it impacts all aspects of human life and activity. Heat transfers are, by nature, classified as conduction, convection (which inserts conduction into fluid mechanics) and radiation. The importance of these three transfer methods has resulted – justifiably – in a separate volume being afforded to each of them. This second volume is dedicated to radiation. After recalling photometry, the calculation of luminance is addressed using the theory of the black body and associated laws: Stefan, Wien. The reciprocal radiation of two surfaces in total influence is discussed extensively, and the case of finished surfaces is also considered. Heat Transfer 2 combines a basic approach with a deeper understanding of the discipline and will therefore appeal to a wide audience, from technician to engineer, from doctoral student to teacher-researcher.

Heat is a branch of thermodynamics that occupies a unique position due to its involvement in the field of practice. Being linked to the management, transport and exchange of energy in thermal form, it impacts all aspects of human life and activity. Heat transfers are, by nature, classified as conduction, convection (which inserts conduction into fluid mechanics) and radiation. The importance of these three transfer methods has resulted – justifiably – in a separate volume being afforded to each of them, with the subject of convection split into two volumes.This third volume is dedicated to convection, more specifically, the foundations of convective transfers. Various angles are considered to cover this topic, including empirical relationships and analytically approaching boundary layers, including the integral methods and numerical approaches. The problem of heat exchangers is presented, without aiming to be an exhaustive treatise. Heat Transfer 3 combines a basic approach with a deeper understanding of the discipline and will therefore appeal to a wide audience, from technician to engineer, from doctoral student to teacher-researcher.

Heat is a branch of thermodynamics that occupies a unique position due to its involvement in the field of practice. Being linked to the management, transport and exchange of energy in thermal form, it impacts all aspects of human life and activity.Heat transfers are, by nature, classified as conduction, convection (which inserts conduction into fluid mechanics) and radiation. The importance of these three transfer methods has resulted – justifiably – in a separate volume being afforded to each of them, with the subject of convection split into two volumes. This fourth volume is dedicated to convection, more specifically, the problem of particular convective transfers. Twophase convection is considered and a more recent and much lesser-known field is presented, that of phase change transfer. Particular significance is given to numerical applications, allowing the reader to handle orders of magnitude, an important point in all physics.Heat Transfer 4 combines a basic approach with a deeper understanding of the discipline and will therefore appeal to a wide audience, from technician to engineer, from doctoral student to teacher-researcher.

The book aims to provide an efficient methodology of solving a fluid mechanics problem. It aims to meet different objectives of the student, the future engineer or scientist. Using simple sizing calculations, and more advanced analytical calculations, the book covers all the essential numerical approaches for solving complex practical problems.

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.

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 andgeometric curvature will find it especially useful. Selected chapters can also be used for advanced courses on the topic.

The 36th Seminaire de Probabilites contains an advanced course on Logarithmic Sobolev Inequalities by A. Guionnet and B. Zegarlinski, as well as two shorter surveys by L. Pastur and N. O'Connell on the theory of random matrices and their links with stochastic processes. The main themes of the other contributions are Logarithmic Sobolev Inequalities, Stochastic Calculus, Martingale Theory and Filtrations. Besides the traditional readership of the Seminaires, this volume will be useful to researchers in statistical mechanics and mathematical finance.

The 37th Seminaire de Probabilites contains A. Lejay's advanced course which is a pedagogical introduction to works by T. Lyons and others on stochastic integrals and SDEs driven by deterministic rough paths. The rest of the volume consists of various articles on topics familiar to regular readers of the Seminaires, including Brownian motion, random environment or scenery, PDEs and SDEs, random matrices and financial random processes.

Besides a series of six articles on Levy processes, Volume 38 of the Seminaire de Probabilites contains contributions whose topics range from analysis of semi-groups to free probability, via martingale theory, Wiener space and Brownian motion, Gaussian processes and matrices, diffusions and their applications to PDEs.As do all previous volumes of this series, it provides an overview on the current state of the art in the research on stochastic processes.

Dealing with the subject of probability theory and statistics, this text includes coverage of: inverse problems; isoperimetry and gaussian analysis; and perturbation methods of the theory of Gibbsian fields.

All the papers in the volume are original research papers, discussing fundamental properties of stochastic processes. The topics under study (martingales, filtrations, path properties, etc. ) represent an important part of the current research performed in 1996-97 by various groups of probabilists in France and abroad.

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.