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Author: Tomasz Komorowski
Publisher: Springer Science & Business Media
ISBN: 364229880X
Category : Mathematics
Languages : en
Pages : 494
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Book Description
The present volume contains the most advanced theories on the martingale approach to central limit theorems. Using the time symmetry properties of the Markov processes, the book develops the techniques that allow us to deal with infinite dimensional models that appear in statistical mechanics and engineering (interacting particle systems, homogenization in random environments, and diffusion in turbulent flows, to mention just a few applications). The first part contains a detailed exposition of the method, and can be used as a text for graduate courses. The second concerns application to exclusion processes, in which the duality methods are fully exploited. The third part is about the homogenization of diffusions in random fields, including passive tracers in turbulent flows (including the superdiffusive behavior). There are no other books in the mathematical literature that deal with this kind of approach to the problem of the central limit theorem. Hence, this volume meets the demand for a monograph on this powerful approach, now widely used in many areas of probability and mathematical physics. The book also covers the connections with and application to hydrodynamic limits and homogenization theory, so besides probability researchers it will also be of interest also to mathematical physicists and analysts.
Author: Tomasz Komorowski
Publisher: Springer Science & Business Media
ISBN: 364229880X
Category : Mathematics
Languages : en
Pages : 494
Get Book Here
Book Description
The present volume contains the most advanced theories on the martingale approach to central limit theorems. Using the time symmetry properties of the Markov processes, the book develops the techniques that allow us to deal with infinite dimensional models that appear in statistical mechanics and engineering (interacting particle systems, homogenization in random environments, and diffusion in turbulent flows, to mention just a few applications). The first part contains a detailed exposition of the method, and can be used as a text for graduate courses. The second concerns application to exclusion processes, in which the duality methods are fully exploited. The third part is about the homogenization of diffusions in random fields, including passive tracers in turbulent flows (including the superdiffusive behavior). There are no other books in the mathematical literature that deal with this kind of approach to the problem of the central limit theorem. Hence, this volume meets the demand for a monograph on this powerful approach, now widely used in many areas of probability and mathematical physics. The book also covers the connections with and application to hydrodynamic limits and homogenization theory, so besides probability researchers it will also be of interest also to mathematical physicists and analysts.
Author:
Publisher: Elsevier
ISBN: 0080479235
Category : Science
Languages : en
Pages : 849
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Book Description
The proceedings of the 2005 les Houches summer school on Mathematical Statistical Physics give and broad and clear overview on this fast developing area of interest to both physicists and mathematicians. - Introduction to a field of math with many interdisciplinary connections in physics, biology, and computer science - Roadmap to the next decade of mathematical statistical mechanics - Volume for reference years to come
Author: Alain-Sol Sznitman
Publisher: Springer Science & Business Media
ISBN: 3662112817
Category : Mathematics
Languages : en
Pages : 366
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Book Description
This book provides an account for the non-specialist of the circle of ideas, results and techniques, which grew out in the study of Brownian motion and random obstacles. It also includes an overview of known results and connections with other areas of random media, taking a highly original and personal approach throughout.
Author: Erwin Bolthausen
Publisher: Birkhäuser
ISBN: 3034881592
Category : Mathematics
Languages : en
Pages : 120
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Book Description
The following notes grew out oflectures held during the DMV-Seminar on Random Media in November 1999 at the Mathematics Research Institute of Oberwolfach, and in February-March 2000 at the Ecole Normale Superieure in Paris. In both places the atmosphere was very friendly and stimulating. The positive response of the audience was encouragement enough to write up these notes. I hope they will carryover the enjoyment of the live lectures. I whole heartedly wish to thank Profs. Matthias Kreck and Jean-Franc;ois Le Gall who were respon sible for these two very enjoyable visits, Laurent Miclo for his comments on an earlier version of these notes, and last but not least Erwin Bolthausen who was my accomplice during the DMV-Seminar. A Brief Introduction The main theme of this series of lectures are "Random motions in random me dia". The subject gathers a variety of probabilistic models often originated from physical sciences such as solid state physics, physical chemistry, oceanography, biophysics . . . , in which typically some diffusion mechanism takes place in an inho mogeneous medium. Randomness appears at two levels. It comes in the description of the motion of the particle diffusing in the medium, this is a rather traditional point of view for probability theory; but it also comes in the very description of the medium in which the diffusion takes place.
Author: David Holcman
Publisher: Springer
ISBN: 3319626272
Category : Mathematics
Languages : en
Pages : 377
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Book Description
This book focuses on the modeling and mathematical analysis of stochastic dynamical systems along with their simulations. The collected chapters will review fundamental and current topics and approaches to dynamical systems in cellular biology. This text aims to develop improved mathematical and computational methods with which to study biological processes. At the scale of a single cell, stochasticity becomes important due to low copy numbers of biological molecules, such as mRNA and proteins that take part in biochemical reactions driving cellular processes. When trying to describe such biological processes, the traditional deterministic models are often inadequate, precisely because of these low copy numbers. This book presents stochastic models, which are necessary to account for small particle numbers and extrinsic noise sources. The complexity of these models depend upon whether the biochemical reactions are diffusion-limited or reaction-limited. In the former case, one needs to adopt the framework of stochastic reaction-diffusion models, while in the latter, one can describe the processes by adopting the framework of Markov jump processes and stochastic differential equations. Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology will appeal to graduate students and researchers in the fields of applied mathematics, biophysics, and cellular biology.
Author: F.H. Clarke
Publisher: Springer Science & Business Media
ISBN: 9401145601
Category : Mathematics
Languages : en
Pages : 614
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Book Description
Recent years have witnessed important developments in those areas of the mathematical sciences where the basic model under study is a dynamical system such as a differential equation or control process. Many of these recent advances were made possible by parallel developments in nonlinear and nonsmooth analysis. The latter subjects, in general terms, encompass differential analysis and optimization theory in the absence of traditional linearity, convexity or smoothness assumptions. In the last three decades it has become increasingly recognized that nonlinear and nonsmooth behavior is naturally present and prevalent in dynamical models, and is therefore significant theoretically. This point of view has guided us in the organizational aspects of this ASI. Our goals were twofold: We intended to achieve "cross fertilization" between mathematicians who were working in a diverse range of problem areas, but who all shared an interest in nonlinear and nonsmooth analysis. More importantly, it was our goal to expose a young international audience (mainly graduate students and recent Ph. D. 's) to these important subjects. In that regard, there were heavy pedagogical demands placed upon the twelve speakers of the ASI, in meeting the needs of such a gathering. The talks, while exposing current areas of research activity, were required to be as introductory and comprehensive as possible. It is our belief that these goals were achieved, and that these proceedings bear this out. Each of the twelve speakers presented a mini-course of four or five hours duration.
Author: Boyan Sirakov
Publisher: World Scientific
ISBN: 9813272899
Category : Mathematics
Languages : en
Pages : 5393
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Book Description
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.
Author: Grigoris Pavliotis
Publisher: Springer Science & Business Media
ISBN: 0387738290
Category : Mathematics
Languages : en
Pages : 314
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Book Description
This introduction to multiscale methods gives you a broad overview of the methods’ many uses and applications. The book begins by setting the theoretical foundations of the methods and then moves on to develop models and prove theorems. Extensive use of examples shows how to apply multiscale methods to solving a variety of problems. Exercises then enable you to build your own skills and put them into practice. Extensions and generalizations of the results presented in the book, as well as references to the literature, are provided in the Discussion and Bibliography section at the end of each chapter.With the exception of Chapter One, all chapters are supplemented with exercises.
Author: Robert C. Dalang
Publisher: Birkhäuser
ISBN: 3034882092
Category : Mathematics
Languages : en
Pages : 310
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Book Description
This volume contains 20 refereed research or review papers presented at the five-day Third Seminar on Stochastic Analysis, Random Fields and Applications which took place at the Centro Stefano Franscini (Monte Verità) in Ascona, Switzerland, from September 20 to 24, 1999. The seminar focused on three topics: fundamental aspects of stochastic analysis, physical modeling, and applications to financial engineering. The third topic was the subject of a mini-symposium on stochastic methods in financial models.
Author: Mark A. Pinsky
Publisher: CRC Press
ISBN: 1000146200
Category : Mathematics
Languages : en
Pages : 476
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Book Description
This volume attempts to exhibit current research in stochastic integration, stochastic differential equations, stochastic optimization and stochastic problems in physics and biology. It includes information on the theory of Dirichlet forms, Feynman integration and the Schrodinger's equation.
