Probability in Banach Spaces: Isoperimetry and Processes (Classics in Mathematics) by Michel Ledoux (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review This book gives an excellent, almost complete account of the whole subject of probability in Banach spaces, a branch of probability theory that has undergone vigorous development… There is no doubt in the reviewer’s mind that this book [has] become a classic. MathSciNetAs the authors state, “this book tries to present some of the main aspects of the theory of probability in Banach spaces, from the foundation of the topic to the latest developments and current research questions”. The authors have succeeded admirably… This very comprehensive book develops a wide variety of the methods existing … in probability in Banach spaces. … It [has] become an event for mathematicians… Zentralblatt MATH From the Back Cover 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. About the Author Michel Ledoux held first a research position with CNRS, and since 1991 is Professor at the University of Toulouse. He is moreover, since 2010, a senior member of the Institut Universitaire de France, having been also a junior member from 1997 to 2002. He has held associate editor appointments for various journals, including the Annals of Probability and Probability Theory and Related Fields (current). His research interests centre on probability, random matrices, logarithmic Sobolev inequalities, probability in Banach spaces.Michel Talagrand has held a research position with the CNRS since 1974. His thesis was directed by Gustave Choquet and his interests revolve around the theory of stochastic processes and probability in Banach spaces, as well as the mathematical theory of spin glasses. He was invited to deliver a lecture at the International Congress of Mathematicians in 1990, and to deliver a plenary lecture at the same congress in 1998. He received the Loeve Prize (1995) and the Fermat Prize (1997) for his work in probability theory. He was elected to the Paris Academy of Sciences in 2004. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is the standard for all who seek detailed information about stochastics in Banach spaces. Written from two of the top researchers in this area, it provides a broad area of topics, a concise treatment of deep results and exhaustive references. Sadly enough, it is out of print now, but I hope for a 2nd edition.

⭐This book is a mathematical classics. You could find important results in Banach space. I could recommend this book to anybody who interested in probability and functional analysis.

⭐Del libro poco hay que decir. Teniendo en cuenta que es del 91, y por tanto no recoge los avances en procesos empíricos y sobre todo concentración de la medida de las décadas siguientes, sigue siendo relevante y da una imagen muy completa de los resultados de teoría de la probabilidad en espacios de Banach de los años 70 y 80.Sobre esta edición sí hay que decir cosas, Springer solo pone el nombre y en realidad la impresión la realiza Amazon directamente bajo pedido. En la web de Springer *no* se ofrece esta edición y tampoco viene en el interior la fecha de publicación sino la de una edición anterior. Me pregunto cuál es la idea de Springer sobre cómo voy a citar el libro. Además, mi ejemplar ha venido mal cortado; pero, aparte de la molestia estética, el contenido es lo que importa.

⭐

⭐The book is very well written and one can easily follow the ideas with only a basic background in measure theoretic probability theory.

⭐The book is a definitely good one but the quality of the book that I have received is not really good. The print quality is really bad and it looks like an offset than a print.

Keywords

Free Download Probability in Banach Spaces: Isoperimetry and Processes (Classics in Mathematics) in PDF format
Probability in Banach Spaces: Isoperimetry and Processes (Classics in Mathematics) PDF Free Download
Download Probability in Banach Spaces: Isoperimetry and Processes (Classics in Mathematics) 2011 PDF Free
Probability in Banach Spaces: Isoperimetry and Processes (Classics in Mathematics) 2011 PDF Free Download
Download Probability in Banach Spaces: Isoperimetry and Processes (Classics in Mathematics) PDF
Free Download Ebook Probability in Banach Spaces: Isoperimetry and Processes (Classics in Mathematics)