Analysis and Geometry of Markov Diffusion Operators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Analysis and Geometry of Markov Diffusion Operators write by Dominique Bakry. This book was released on 2013-11-18. Analysis and Geometry of Markov Diffusion Operators available in PDF, EPUB and Kindle. 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.
On the Geometry of Diffusion Operators and Stochastic Flows
On the Geometry of Diffusion Operators and Stochastic Flows - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On the Geometry of Diffusion Operators and Stochastic Flows write by K.D. Elworthy. This book was released on 2007-01-05. On the Geometry of Diffusion Operators and Stochastic Flows available in PDF, EPUB and Kindle. Stochastic differential equations, and Hoermander form representations of diffusion operators, can determine a linear connection associated to the underlying (sub)-Riemannian structure. This is systematically described, together with its invariants, and then exploited to discuss qualitative properties of stochastic flows, and analysis on path spaces of compact manifolds with diffusion measures. This should be useful to stochastic analysts, especially those with interests in stochastic flows, infinite dimensional analysis, or geometric analysis, and also to researchers in sub-Riemannian geometry. A basic background in differential geometry is assumed, but the construction of the connections is very direct and itself gives an intuitive and concrete introduction. Knowledge of stochastic analysis is also assumed for later chapters.
Geometric Aspects of Functional Analysis
Geometric Aspects of Functional Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Aspects of Functional Analysis write by Bo'az Klartag. This book was released on 2020-06-20. Geometric Aspects of Functional Analysis available in PDF, EPUB and Kindle. Continuing the theme of the previous volumes, these seminar notes reflect general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. Two classical topics represented are the Concentration of Measure Phenomenon in the Local Theory of Banach Spaces, which has recently had triumphs in Random Matrix Theory, and the Central Limit Theorem, one of the earliest examples of regularity and order in high dimensions. Central to the text is the study of the Poincaré and log-Sobolev functional inequalities, their reverses, and other inequalities, in which a crucial role is often played by convexity assumptions such as Log-Concavity. The concept and properties of Entropy form an important subject, with Bourgain's slicing problem and its variants drawing much attention. Constructions related to Convexity Theory are proposed and revisited, as well as inequalities that go beyond the Brunn–Minkowski theory. One of the major current research directions addressed is the identification of lower-dimensional structures with remarkable properties in rather arbitrary high-dimensional objects. In addition to functional analytic results, connections to Computer Science and to Differential Geometry are also discussed.
Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)
Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) write by Boyan Sirakov. This book was released on 2019-02-27. Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) available in PDF, EPUB and Kindle. The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Geometric Analysis and Nonlinear Partial Differential Equations
Geometric Analysis and Nonlinear Partial Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Analysis and Nonlinear Partial Differential Equations write by Stefan Hildebrandt. This book was released on 2012-12-06. Geometric Analysis and Nonlinear Partial Differential Equations available in PDF, EPUB and Kindle. This book is not a textbook, but rather a coherent collection of papers from the field of partial differential equations. Nevertheless we believe that it may very well serve as a good introduction into some topics of this classical field of analysis which, despite of its long history, is highly modem and well prospering. Richard Courant wrote in 1950: "It has always been a temptationfor mathematicians to present the crystallized product of their thought as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives; live mathematical development springs from specific natural problems which can be easily understood, but whose solutions are difficult and demand new methods or more general significance. " We think that many, if not all, papers of this book are written in this spirit and will give the reader access to an important branch of analysis by exhibiting interest ing problems worth to be studied. Most of the collected articles have an extensive introductory part describing the history of the presented problems as well as the state of the art and offer a well chosen guide to the literature. This way the papers became lengthier than customary these days, but the level of presentation is such that an advanced graduate student should find the various articles both readable and stimulating.
