Analysis and Geometry of Markov Diffusion Operators
1st Edition
Published on 27. November 2013
Book
Hardback
XX, 552 pages
978-3-319-00226-2 (ISBN)
Description
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 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.
More details
Product info
HC runder Rücken kaschiert
Series
Language
English
Place of publication
Cham
Switzerland
Target group
Research
Product notice
Laminated cover
Illustrations
black & white illustrations
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 36 mm
Weight
1011 gr
ISBN-13
978-3-319-00226-2 (9783319002262)
DOI
10.1007/978-3-319-00227-9
Schweitzer Classification
Other editions
Additional editions
Dominique Bakry | Ivan Gentil | Michel Ledoux
Analysis and Geometry of Markov Diffusion Operators
Book
08/2016
Springer
€149.79
Shipment within 10-15 days
Dominique Bakry | Ivan Gentil | Michel Ledoux
Analysis and Geometry of Markov Diffusion Operators
E-Book
11/2013
1st Edition
Springer
€139.09
Available for download
Persons
Dominique Bakry held his first research position at the CNRS at the University of Strasbourg, and since 1988 has been a professor at the University of Toulouse. Moreover, since 2004 he has been a senior member of the Institut Universitaire de France. He was editor of the journal Potential Analysis. His research interests center on probability, analysis of Markov operators, differential geometry and orthonormal polynomials.
Ivan Gentil held his first position at the University of Paris-Dauphine in 2003 and since 2010 has been a professor at the University of Lyon. His research interests center on analysis, probability, partial differential equations and functional inequalities such as logarithmic Sobolev inequalities.
Michel Ledoux held his first research position at the CNRS, and since 1991 has been a professor at the University of Toulouse. Since 2010 he has been a senior member of the Institut Universitaire de France, having been a junior member from 1997 to 2002. He has been associate editor for various journals including the Annals of Probability and Probability Theory and Related Fields, and is currently chief editor of the Electronic Journal of Probability. His research interests center on probability theory and functional analysis, measure concentration, diffusion operators and functional inequalities, random matrices, probability in Banach spaces.
Ivan Gentil held his first position at the University of Paris-Dauphine in 2003 and since 2010 has been a professor at the University of Lyon. His research interests center on analysis, probability, partial differential equations and functional inequalities such as logarithmic Sobolev inequalities.
Michel Ledoux held his first research position at the CNRS, and since 1991 has been a professor at the University of Toulouse. Since 2010 he has been a senior member of the Institut Universitaire de France, having been a junior member from 1997 to 2002. He has been associate editor for various journals including the Annals of Probability and Probability Theory and Related Fields, and is currently chief editor of the Electronic Journal of Probability. His research interests center on probability theory and functional analysis, measure concentration, diffusion operators and functional inequalities, random matrices, probability in Banach spaces.
Content
Introduction.- Part I Markov semigroups, basics and examples: 1.Markov semigroups.- 2.Model examples.- 3.General setting.- Part II Three model functional inequalities: 4.Poincaré inequalities.- 5.Logarithmic Sobolev inequalities.- 6.Sobolev inequalities.- Part III Related functional, isoperimetric and transportation inequalities: 7.Generalized functional inequalities.- 8.Capacity and isoperimetry-type inequalities.- 9.Optimal transportation and functional inequalities.- Part IV Appendices: A.Semigroups of bounded operators on a Banach space.- B.Elements of stochastic calculus.- C.Some basic notions in differential and Riemannian geometry.- Notations and list of symbols.- Bibliography.- Index.