Probability And Analysis In Interacting Physical Systems

Author : Peter Friz,Wolfgang König,Chiranjib Mukherjee,Stefano Olla
Publisher : Springer
Page : 294 pages
File Size : 52,7 Mb
Release : 2019-05-24
Category : Mathematics
ISBN : 9783030153380

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Probability and Analysis in Interacting Physical Systems by Peter Friz,Wolfgang König,Chiranjib Mukherjee,Stefano Olla Pdf

This Festschrift on the occasion of the 75th birthday of S.R.S. Varadhan, one of the most influential researchers in probability of the last fifty years, grew out of a workshop held at the Technical University of Berlin, 15–19 August, 2016. This volume contains ten research articles authored by several of Varadhan's former PhD students or close collaborators. The topics of the contributions are more or less closely linked with some of Varadhan's deepest interests over the decades: large deviations, Markov processes, interacting particle systems, motions in random media and homogenization, reaction-diffusion equations, and directed last-passage percolation. The articles present original research on some of the most discussed current questions at the boundary between analysis and probability, with an impact on understanding phenomena in physics. This collection will be of great value to researchers with an interest in models of probability-based statistical mechanics.

Author : Jean-Dominique Deuschel,Barbara Gentz,Wolfgang König,Max von Renesse,Michael Scheutzow,Uwe Schmock
Publisher : Springer Science & Business Media
Page : 518 pages
File Size : 40,9 Mb
Release : 2012-04-23
Category : Mathematics
ISBN : 9783642238116

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Probability in Complex Physical Systems by Jean-Dominique Deuschel,Barbara Gentz,Wolfgang König,Max von Renesse,Michael Scheutzow,Uwe Schmock Pdf

Probabilistic approaches have played a prominent role in the study of complex physical systems for more than thirty years. This volume collects twenty articles on various topics in this field, including self-interacting random walks and polymer models in random and non-random environments, branching processes, Parisi formulas and metastability in spin glasses, and hydrodynamic limits for gradient Gibbs models. The majority of these articles contain original results at the forefront of contemporary research; some of them include review aspects and summarize the state-of-the-art on topical issues – one focal point is the parabolic Anderson model, which is considered with various novel aspects including moving catalysts, acceleration and deceleration and fron propagation, for both time-dependent and time-independent potentials. The authors are among the world’s leading experts. This Festschrift honours two eminent researchers, Erwin Bolthausen and Jürgen Gärtner, whose scientific work has profoundly influenced the field and all of the present contributions.

Author : Victor Chulaevsky,Yuri Suhov
Publisher : Springer Science & Business Media
Page : 246 pages
File Size : 46,9 Mb
Release : 2013-09-20
Category : Mathematics
ISBN : 9781461482260

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Multi-scale Analysis for Random Quantum Systems with Interaction by Victor Chulaevsky,Yuri Suhov Pdf

The study of quantum disorder has generated considerable research activity in mathematics and physics over past 40 years. While single-particle models have been extensively studied at a rigorous mathematical level, little was known about systems of several interacting particles, let alone systems with positive spatial particle density. Creating a consistent theory of disorder in multi-particle quantum systems is an important and challenging problem that largely remains open. Multi-scale Analysis for Random Quantum Systems with Interaction presents the progress that had been recently achieved in this area. The main focus of the book is on a rigorous derivation of the multi-particle localization in a strong random external potential field. To make the presentation accessible to a wider audience, the authors restrict attention to a relatively simple tight-binding Anderson model on a cubic lattice Zd. This book includes the following cutting-edge features: an introduction to the state-of-the-art single-particle localization theory an extensive discussion of relevant technical aspects of the localization theory a thorough comparison of the multi-particle model with its single-particle counterpart a self-contained rigorous derivation of both spectral and dynamical localization in the multi-particle tight-binding Anderson model. Required mathematical background for the book includes a knowledge of functional calculus, spectral theory (essentially reduced to the case of finite matrices) and basic probability theory. This is an excellent text for a year-long graduate course or seminar in mathematical physics. It also can serve as a standard reference for specialists.

Author : Thomas M. Liggett
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 55,9 Mb
Release : 1999-08-13
Category : Education
ISBN : 3540659951

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Stochastic Interacting Systems: Contact, Voter and Exclusion Processes by Thomas M. Liggett Pdf

Interactive Particle Systems is a branch of Probability Theory with close connections to Mathematical Physics and Mathematical Biology. In 1985, the author wrote a book (T. Liggett, Interacting Particle System, ISBN 3-540-96069) that treated the subject as it was at that time. The present book takes three of the most important models in the area, and traces advances in our understanding of them since 1985. In so doing, many of the most useful techniques in the field are explained and developed, so that they can be applied to other models and in other contexts. Extensive Notes and References sections discuss other work on these and related models. Readers are expected to be familiar with analysis and probability at the graduate level, but it is not assumed that they have mastered the material in the 1985 book. This book is intended for graduate students and researchers in Probability Theory, and in related areas of Mathematics, Biology and Physics.

Author : Vladas Sidoravicius
Publisher : Springer Nature
Page : 341 pages
File Size : 47,9 Mb
Release : 2019-10-17
Category : Mathematics
ISBN : 9789811503023

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Sojourns in Probability Theory and Statistical Physics - III by Vladas Sidoravicius Pdf

Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for nearly half a century. This three-volume set is a celebration of the far-reaching scientific impact of his work. It consists of articles by Chuck’s collaborators and colleagues across a number of the fields to which he has made contributions of fundamental significance. This publication was conceived during a conference in 2016 at NYU Shanghai that coincided with Chuck's 70th birthday. The sub-titles of the three volumes are: I. Spin Glasses and Statistical Mechanics II. Brownian Web and Percolation III. Interacting Particle Systems and Random Walks The articles in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate students and researchers who seek initiation and inspiration in Probability Theory and Statistical Physics.

Author : Achim Klenke
Publisher : Springer Nature
Page : 716 pages
File Size : 53,5 Mb
Release : 2020-10-30
Category : Mathematics
ISBN : 9783030564025

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Probability Theory by Achim Klenke Pdf

This popular textbook, now in a revised and expanded third edition, presents a comprehensive course in modern probability theory. Probability plays an increasingly important role not only in mathematics, but also in physics, biology, finance and computer science, helping to understand phenomena such as magnetism, genetic diversity and market volatility, and also to construct efficient algorithms. Starting with the very basics, this textbook covers a wide variety of topics in probability, including many not usually found in introductory books, such as: limit theorems for sums of random variables martingales percolation Markov chains and electrical networks construction of stochastic processes Poisson point process and infinite divisibility large deviation principles and statistical physics Brownian motion stochastic integrals and stochastic differential equations. The presentation is self-contained and mathematically rigorous, with the material on probability theory interspersed with chapters on measure theory to better illustrate the power of abstract concepts. This third edition has been carefully extended and includes new features, such as concise summaries at the end of each section and additional questions to encourage self-reflection, as well as updates to the figures and computer simulations. With a wealth of examples and more than 290 exercises, as well as biographical details of key mathematicians, it will be of use to students and researchers in mathematics, statistics, physics, computer science, economics and biology.

Author : Stefania Ugolini,Marco Fuhrman,Elisa Mastrogiacomo,Paola Morando,Barbara Rüdiger
Publisher : Springer Nature
Page : 273 pages
File Size : 53,9 Mb
Release : 2022-02-09
Category : Mathematics
ISBN : 9783030874322

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Geometry and Invariance in Stochastic Dynamics by Stefania Ugolini,Marco Fuhrman,Elisa Mastrogiacomo,Paola Morando,Barbara Rüdiger Pdf

This book grew out of the Random Transformations and Invariance in Stochastic Dynamics conference held in Verona from the 25th to the 28th of March 2019 in honour of Sergio Albeverio. It presents the new area of studies concerning invariance and symmetry properties of finite and infinite dimensional stochastic differential equations.This area constitutes a natural, much needed, extension of the theory of classical ordinary and partial differential equations, where the reduction theory based on symmetry and invariance of such classical equations has historically proved to be very important both for theoretical and numerical studies and has given rise to important applications. The purpose of the present book is to present the state of the art of the studies on stochastic systems from this point of view, present some of the underlying fundamental ideas and methods involved, and to outline the main lines for future developments. The main focus is on bridging the gap between deterministic and stochastic approaches, with the goal of contributing to the elaboration of a unified theory that will have a great impact both from the theoretical point of view and the point of view of applications. The reader is a mathematician or a theoretical physicist. The main discipline is stochastic analysis with profound ideas coming from Mathematical Physics and Lie’s Group Geometry. While the audience consists essentially of academicians, the reader can also be a practitioner with Ph.D., who is interested in efficient stochastic modelling.

Author : G. R. Grimmett
Publisher : Unknown
Page : 340 pages
File Size : 55,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401583277

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Probability and Phase Transition by G. R. Grimmett Pdf

Author : A.B. Cruzeiro,J.-C. Zambrini
Publisher : Springer Science & Business Media
Page : 162 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201274

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Stochastic Analysis and Mathematical Physics by A.B. Cruzeiro,J.-C. Zambrini Pdf

This volume represents the outgrowth of an ongoing workshop on stochastic analysis held in Lisbon. The nine survey articles in the volume extend concepts from classical probability and stochastic processes to a number of areas of mathematical physics. It is a good reference text for researchers and advanced students in the fields of probability, stochastic processes, analysis, geometry, mathematical physics, and physics. Key topics covered include: nonlinear stochastic wave equations, completely positive maps, Mehler-type semigroups on Hilbert spaces, entropic projections, and many others.

Author : Ettore Vitali,Mario Motta,Davide Emilio Galli
Publisher : Springer
Page : 235 pages
File Size : 44,7 Mb
Release : 2018-06-13
Category : Science
ISBN : 9783319905150

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Theory and Simulation of Random Phenomena by Ettore Vitali,Mario Motta,Davide Emilio Galli Pdf

The purpose of this book is twofold: first, it sets out to equip the reader with a sound understanding of the foundations of probability theory and stochastic processes, offering step-by-step guidance from basic probability theory to advanced topics, such as stochastic differential equations, which typically are presented in textbooks that require a very strong mathematical background. Second, while leading the reader on this journey, it aims to impart the knowledge needed in order to develop algorithms that simulate realistic physical systems. Connections with several fields of pure and applied physics, from quantum mechanics to econophysics, are provided. Furthermore, the inclusion of fully solved exercises will enable the reader to learn quickly and to explore topics not covered in the main text. The book will appeal especially to graduate students wishing to learn how to simulate physical systems and to deepen their knowledge of the mathematical framework, which has very deep connections with modern quantum field theory.

Author : Y. M. Guttmann
Publisher : Cambridge University Press
Page : 283 pages
File Size : 40,7 Mb
Release : 1999-07-13
Category : Mathematics
ISBN : 9780521621281

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The Concept of Probability in Statistical Physics by Y. M. Guttmann Pdf

A most systematic study of how to interpret probabilistic assertions in the context of statistical mechanics.

Author : Anton Bovier,David Brydges,Amin Coja-Oghlan,Dmitry Ioffe,Gregory F. Lawler
Publisher : Springer
Page : 239 pages
File Size : 55,9 Mb
Release : 2015-09-21
Category : Science
ISBN : 9783319193397

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Random Walks, Random Fields, and Disordered Systems by Anton Bovier,David Brydges,Amin Coja-Oghlan,Dmitry Ioffe,Gregory F. Lawler Pdf

Focusing on the mathematics that lies at the intersection of probability theory, statistical physics, combinatorics and computer science, this volume collects together lecture notes on recent developments in the area. The common ground of these subjects is perhaps best described by the three terms in the title: Random Walks, Random Fields and Disordered Systems. The specific topics covered include a study of Branching Brownian Motion from the perspective of disordered (spin-glass) systems, a detailed analysis of weakly self-avoiding random walks in four spatial dimensions via methods of field theory and the renormalization group, a study of phase transitions in disordered discrete structures using a rigorous version of the cavity method, a survey of recent work on interacting polymers in the ballisticity regime and, finally, a treatise on two-dimensional loop-soup models and their connection to conformally invariant systems and the Gaussian Free Field. The notes are aimed at early graduate students with a modest background in probability and mathematical physics, although they could also be enjoyed by seasoned researchers interested in learning about recent advances in the above fields.

Author : Jean-Dominique Deuschel
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 41,9 Mb
Release : 2005-01-12
Category : Computers
ISBN : 3540230335

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Interacting Stochastic Systems by Jean-Dominique Deuschel Pdf

The Research Network on "Interacting stochastic systems of high complexity" set up by the German Research Foundation aimed at exploring and developing connections between research in infinite-dimensional stochastic analysis, statistical physics, spatial population models from mathematical biology, complex models of financial markets or of stochastic models interacting with other sciences. This book presents a structured collection of papers on the core topics, written at the close of the 6-year programme by the research groups who took part in it. The structure chosen highlights the interweaving of certain themes and certain interconnections discovered through the joint work. This yields a reference work on results and methods that will be useful to all who work between applied probability and the physical, economic, and life sciences.

Author : J. Laurie Snell
Publisher : CRC Press
Page : 400 pages
File Size : 40,8 Mb
Release : 1995-04-18
Category : Mathematics
ISBN : 0849380731

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Topics in Contemporary Probability and Its Applications by J. Laurie Snell Pdf

Probability theory has grown from a modest study of simple games of change to a subject with application in almost every branch of knowledge and science. In this exciting book, a number of distinguished probabilists discuss their current work and applications in an easily understood manner. Chapters show that new directions in probability have been suggested by the application of probability to other fields and other disciplines of mathematics. The study of polymer chains in chemistry led to the study of self-avoiding random walks; the study of the Ising model in physics and models for epidemics in biology led to the study of the probability theory of interacting particle systems. The stochastic calculus has allowed probabilists to solve problems in classical analysis, in theory of investment, and in engineering. The mathematical formulation of game theory has led to new insights into decisions under uncertainty. These new developments in probability are vividly illustrated throughout the book.

Author : Habib Zaidi
Publisher : Springer Science & Business Media
Page : 593 pages
File Size : 46,9 Mb
Release : 2006-07-11
Category : Science
ISBN : 9780387254449

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Quantitative Analysis in Nuclear Medicine Imaging by Habib Zaidi Pdf

This book provides a review of image analysis techniques as they are applied in the field of diagnostic and therapeutic nuclear medicine. Driven in part by the remarkable sophistication of nuclear medicine instrumentation and - crease in computing power and its ready and inexpensive availability, this is a relatively new yet rapidly expanding field. Likewise, although the use of nuclear imaging for diagnosis and therapy has origins dating back almost to the pioneering work of Dr G. de Hevesy, quantitative imaging has only recently emerged as a promising approach for diagnosis and therapy of many diseases. An effort has, therefore, been made to place the reviews provided in this book in a broader context. The effort to do this is reflected by the inclusion of introductory chapters that address basic principles of nuclear medicine instrumentation and dual-modality imaging, followed by overview of issues that are closely related to quantitative nuclear imaging and its potential role in diagnostic and therapeutic applications. A brief overview of each chapter is provided below. Chapter 1 presents a general overview of nuclear medicine imaging physics and instrumentation including planar scintigraphy, single-photon emission computed tomography (SPECT) and positron emission tomography (PET). Nowadays, patients’ diagnosis and therapy is rarely done without the use of imaging technology. As such, imaging considerations are incorporated in almost every chapter of the book. The development of dual-modality - aging systems is an emerging research field, which is addressed in chapter 2.