Analysis and Geometry of Markov Diffusion Operators

  • Dominique Bakry
  • Ivan Gentil
  • Michel Ledoux
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 348)

Table of contents

  1. Front Matter
    Pages I-XX
  2. Markov Semigroups, Basics and Examples

    1. Front Matter
      Pages 1-1
    2. Dominique Bakry, Ivan Gentil, Michel Ledoux
      Pages 3-75
    3. Dominique Bakry, Ivan Gentil, Michel Ledoux
      Pages 77-118
    4. Dominique Bakry, Ivan Gentil, Michel Ledoux
      Pages 119-174
  3. Three Model Functional Inequalities

    1. Front Matter
      Pages 175-175
    2. Dominique Bakry, Ivan Gentil, Michel Ledoux
      Pages 177-233
    3. Dominique Bakry, Ivan Gentil, Michel Ledoux
      Pages 235-275
    4. Dominique Bakry, Ivan Gentil, Michel Ledoux
      Pages 277-343
  4. Related Functional, Isoperimetric and Transportation Inequalities

    1. Front Matter
      Pages 345-345
    2. Dominique Bakry, Ivan Gentil, Michel Ledoux
      Pages 347-389
    3. Dominique Bakry, Ivan Gentil, Michel Ledoux
      Pages 391-431
    4. Dominique Bakry, Ivan Gentil, Michel Ledoux
      Pages 433-469
  5. Back Matter
    Pages 471-552

About this book

Introduction

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.

Keywords

39B62, 39B72, 47D07, 53C21 Markov operators curvature dimension condition diffusion operators functional inequalities

Authors and affiliations

  • Dominique Bakry
    • 1
  • Ivan Gentil
    • 2
  • Michel Ledoux
    • 3
  1. 1.Institut de Mathématiques de Toulouse, Université de Toulouse and Institut Universitaire de FranceToulouseFrance
  2. 2.Université Claude Bernard Lyon 1 Institut Camille JordanVilleurbanneFrance
  3. 3.Institut de Mathématiques de Toulouse, Université de Toulouse and Institut Universitaire de FranceToulouseFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-00227-9
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-00226-2
  • Online ISBN 978-3-319-00227-9
  • Series Print ISSN 0072-7830
  • Series Online ISSN 2196-9701
  • About this book