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The Logarithmic Sobolev Inequality In Infinite Dimensions
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Book Synopsis An Initiation to Logarithmic Sobolev Inequalities by : Gilles Royer
Download or read book An Initiation to Logarithmic Sobolev Inequalities written by Gilles Royer and published by American Mathematical Soc.. This book was released on 2007 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to logarithmic Sobolev inequalities with some important applications to mathematical statistical physics. Royer begins by gathering and reviewing the necessary background material on selfadjoint operators, semigroups, Kolmogorov diffusion processes, and solutions of stochastic differential equations.
Book Synopsis Finite and Infinite Dimensional Analysis in Honor of Leonard Gross by : Hui-Hsiung Kuo
Download or read book Finite and Infinite Dimensional Analysis in Honor of Leonard Gross written by Hui-Hsiung Kuo and published by American Mathematical Soc.. This book was released on 2003 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the special session in honor of Leonard Gross held at the annual Joint Mathematics Meetings in New Orleans (LA). The speakers were specialists in a variety of fields, and many were Professor Gross's former Ph.D. students and their descendants. Papers in this volume present results from several areas of mathematics. They illustrate applications of powerful ideas that originated in Gross's work and permeate diverse fields. Topics include stochastic partial differential equations, white noise analysis, Brownian motion, Segal-Bargmann analysis, heat kernels, and some applications. The volume should be useful to graduate students and researchers. It provides perspective on current activity and on central ideas and techniques in the topics covered.
Book Synopsis Mathematical Foundations of Infinite-Dimensional Statistical Models by : Evarist Giné
Download or read book Mathematical Foundations of Infinite-Dimensional Statistical Models written by Evarist Giné and published by Cambridge University Press. This book was released on 2021-03-25 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: In nonparametric and high-dimensional statistical models, the classical Gauss–Fisher–Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In a final chapter the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions. Winner of the 2017 PROSE Award for Mathematics.
Book Synopsis Seminaire de Probabilites XXXIII by : J. Azema
Download or read book Seminaire de Probabilites XXXIII written by J. Azema and published by Springer. This book was released on 2006-11-14 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Besides topics traditionally found in the Sminaire de Probabilits (Martingale Theory, Stochastic Processes, questions of general interest in Probability Theory), this volume XXXIII presents nine contributions to the study of filtrations up to isomorphism. It also contains three graduate courses: Dynamics of stochastic algorithms, by M. Benaim; Simulated annealing algorithms and Markov chains with rare transitions, by O. Catoni; and Concentration of measure and logarithmic Sobolev inequalities, by M. Ledoux. These up to date courses present the state of the art in three matters of interest to students in theoretical or applied Probability Theory, and to researchers as well.
Book Synopsis Probability Models In Mathematical Physics - Proceedings Of The Conference by : Gregory J Morrow
Download or read book Probability Models In Mathematical Physics - Proceedings Of The Conference written by Gregory J Morrow and published by World Scientific. This book was released on 1991-01-14 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conference proceedings includes discussions on state-of-the-art developments in an area being cross fertilized by both probability and mathematical physics. The physics emphasis represents a vision of exciting interplay between physics and probability.Important new results on the following areas are presented: self avoiding random walk, stochastic geometry on loop groups, percolation, spin systems, magnetism, spin glasses, static disorder, gauge field theory, functional integration and quantum field theory.
Book Synopsis Stochastic Processes, Physics and Geometry: New Interplays. I by : Sergio Albeverio
Download or read book Stochastic Processes, Physics and Geometry: New Interplays. I written by Sergio Albeverio and published by American Mathematical Soc.. This book was released on 2000 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume and "IStochastic Processes, Physics and Geometry: New Interplays II" present state-of-the-art research currently unfolding at the interface between mathematics and physics. Included are select articles from the international conference held in Leipzig (Germany) in honor of Sergio Albeverio's sixtieth birthday. The theme of the conference, "Infinite Dimensional (Stochastic) Analysis and Quantum Physics", was chosen to reflect Albeverio's wide-ranging scientific interests. The articles in these books reflect that broad range of interests and provide a detailed overview highlighting the deep interplay among stochastic processes, mathematical physics, and geometry. The contributions are written by internationally recognized experts in the fields of stochastic analysis, linear and nonlinear (deterministic and stochastic) PDEs, infinite dimensional analysis, functional analysis, commutative and noncommutative probability theory, integrable systems, quantum and statistical mechanics, geometric quantization, and neural networks. Also included are applications in biology and other areas. Most of the contributions are high-level research papers. However, there are also some overviews on topics of general interest. The articles selected for publication in these volumes were specifically chosen to introduce readers to advanced topics, to emphasize interdisciplinary connections, and to stress future research directions. Volume I contains contributions from invited speakers; Volume II contains additional contributed papers. Members of the Canadian Mathematical Society may order at the AMS member price.
Book Synopsis Analysis and Geometry of Markov Diffusion Operators by : Dominique Bakry
Download or read book Analysis and Geometry of Markov Diffusion Operators written by Dominique Bakry and published by Springer Science & Business Media. This book was released on 2013-11-18 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Diffusion, Quantum Theory, and Radically Elementary Mathematics. (MN-47) by : William G. Faris
Download or read book Diffusion, Quantum Theory, and Radically Elementary Mathematics. (MN-47) written by William G. Faris and published by Princeton University Press. This book was released on 2014-09-08 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book's inspiration is Princeton University mathematics professor Edward Nelson's influential work in probability, functional analysis, nonstandard analysis, stochastic mechanics, and logic. The book can be used as a tutorial or reference, or read for pleasure by anyone interested in the role of mathematics in science. Because of the application of diffusive motion to quantum theory, it will interest physicists as well as mathematicians. The introductory chapter describes the interrelationships between the various themes, many of which were first brought to light by Edward Nelson. In his writing and conversation, Nelson has always emphasized and relished the human aspect of mathematical endeavor. In his intellectual world, there is no sharp boundary between the mathematical, the cultural, and the spiritual. It is fitting that the final chapter provides a mathematical perspective on musical theory, one that reveals an unexpected connection with some of the book's main themes.
Book Synopsis Recent Developments in Infinite-Dimensional Analysis and Quantum Probability by : Luigi Accardi
Download or read book Recent Developments in Infinite-Dimensional Analysis and Quantum Probability written by Luigi Accardi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent Developments in Infinite-Dimensional Analysis and Quantum Probability is dedicated to Professor Takeyuki Hida on the occasion of his 70th birthday. The book is more than a collection of articles. In fact, in it the reader will find a consistent editorial work, devoted to attempting to obtain a unitary picture from the different contributions and to give a comprehensive account of important recent developments in contemporary white noise analysis and some of its applications. For this reason, not only the latest results, but also motivations, explanations and connections with previous work have been included. The wealth of applications, from number theory to signal processing, from optimal filtering to information theory, from the statistics of stationary flows to quantum cable equations, show the power of white noise analysis as a tool. Beyond these, the authors emphasize its connections with practically all branches of contemporary probability, including stochastic geometry, the structure theory of stationary Gaussian processes, Neumann boundary value problems, and large deviations.
Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.
Book Synopsis Dirichlet Forms and Stochastic Processes by : Zhiming Ma
Download or read book Dirichlet Forms and Stochastic Processes written by Zhiming Ma and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Book Synopsis Women in Analysis and PDE by : Marianna Chatzakou
Download or read book Women in Analysis and PDE written by Marianna Chatzakou and published by Springer Nature. This book was released on with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective by : René Carmona
Download or read book Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective written by René Carmona and published by Springer Science & Business Media. This book was released on 2007-05-22 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the mathematical issues that arise in modeling the interest rate term structure by casting the interest-rate models as stochastic evolution equations in infinite dimensions. The text includes a crash course on interest rates, a self-contained introduction to infinite dimensional stochastic analysis, and recent results in interest rate theory. From the reviews: "A wonderful book. The authors present some cutting-edge math." --WWW.RISKBOOK.COM
Download or read book Dirichlet Forms written by E. Fabes and published by Springer. This book was released on 2006-11-15 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Dirichlet forms has witnessed recently some very important developments both in theoretical foundations and in applications (stochasticprocesses, quantum field theory, composite materials,...). It was therefore felt timely to have on this subject a CIME school, in which leading experts in the field would present both the basic foundations of the theory and some of the recent applications. The six courses covered the basic theory and applications to: - Stochastic processes and potential theory (M. Fukushima and M. Roeckner) - Regularity problems for solutions to elliptic equations in general domains (E. Fabes and C. Kenig) - Hypercontractivity of semigroups, logarithmic Sobolev inequalities and relation to statistical mechanics (L. Gross and D. Stroock). The School had a constant and active participation of young researchers, both from Italy and abroad.
Book Synopsis Inequalities: A Journey into Linear Analysis by : D. J. H. Garling
Download or read book Inequalities: A Journey into Linear Analysis written by D. J. H. Garling and published by Cambridge University Press. This book was released on 2007-07-05 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a wealth of inequalities used in linear analysis, and explains in detail how they are used. The book begins with Cauchy's inequality and ends with Grothendieck's inequality, in between one finds the Loomis-Whitney inequality, maximal inequalities, inequalities of Hardy and of Hilbert, hypercontractive and logarithmic Sobolev inequalities, Beckner's inequality, and many, many more. The inequalities are used to obtain properties of function spaces, linear operators between them, and of special classes of operators such as absolutely summing operators. This textbook complements and fills out standard treatments, providing many diverse applications: for example, the Lebesgue decomposition theorem and the Lebesgue density theorem, the Hilbert transform and other singular integral operators, the martingale convergence theorem, eigenvalue distributions, Lidskii's trace formula, Mercer's theorem and Littlewood's 4/3 theorem. It will broaden the knowledge of postgraduate and research students, and should also appeal to their teachers, and all who work in linear analysis.
Book Synopsis First International Congress of Chinese Mathematicians by : Stephen Shing-Toung Yau
Download or read book First International Congress of Chinese Mathematicians written by Stephen Shing-Toung Yau and published by American Mathematical Soc.. This book was released on 2001 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Congress of Mathematicians was an historical event that was held at the Morningside Center of Mathematics of the Chinese Academy of Sciences (Beijing). It was the first occasion where Chinese mathematicians from all over the world gathered to present their research. The Morningside Mathematics lectures were given by R. Borcherds, J. Coates, R. Graham, and D. Stroock. Other distinguished speakers included J.-P. Bourguignon, J. Jöst, M. Taylor, and S. L. Lee. Topics covered in the volume include algebra and representation theory, algebraic geometry, number theory and automorphic forms, Riemannian geometry and geometric analysis, mathematical physics, topology, complex analysis and complex geometry, computational mathematics, and combinatorics. Titles in this series are copublished with International Press, Cambridge, MA.
Book Synopsis Mathematical Quantum Field Theory and Related Topics by : Joel S. Feldman
Download or read book Mathematical Quantum Field Theory and Related Topics written by Joel S. Feldman and published by American Mathematical Soc.. This book was released on 1988 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for researchers and advanced graduate students in mathematical physics, this book constitutes the proceedings of a conference on mathematical quantum field theory and related topics. The conference was held at the Centre de Recherches Matheematiques of the Universite de Montreal in September 1987.
