Probability and Analysis in Interacting Physical Systems

Probability and Analysis in Interacting Physical Systems

Author: Peter Friz

Publisher: Springer

Published: 2019-05-24

Total Pages: 303

ISBN-13: 303015338X

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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.


Analysis and Probability

Analysis and Probability

Author: Palle E. T. Jorgensen

Publisher: Springer Science & Business Media

Published: 2007-10-17

Total Pages: 320

ISBN-13: 0387330828

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Combines analysis and tools from probability, harmonic analysis, operator theory, and engineering (signal/image processing) Interdisciplinary focus with hands-on approach, generous motivation and new pedagogical techniques Numerous exercises reinforce fundamental concepts and hone computational skills Separate sections explain engineering terms to mathematicians and operator theory to engineers Fills a gap in the literature


Geometry and Invariance in Stochastic Dynamics

Geometry and Invariance in Stochastic Dynamics

Author: Stefania Ugolini

Publisher: Springer Nature

Published: 2022-02-09

Total Pages: 273

ISBN-13: 303087432X

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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.


Analysis, Probability and Mathematical Physics on Fractals

Analysis, Probability and Mathematical Physics on Fractals

Author: Patricia Alonso Ruiz

Publisher:

Published: 2020

Total Pages: 573

ISBN-13: 9789811215537

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"In the 50 years since Mandelbrot identified the fractality of coastlines, mathematicians and physicists have developed a rich and beautiful theory describing the interplay between analytic, geometric and probabilistic aspects of the mathematics of fractals. Using classical and abstract analytic tools developed by Cantor, Hausdorff, and Sierpinski, they have sought to address fundamental questions: How can we measure the size of a fractal set? How do waves and heat travel on irregular structures? How are analysis, geometry and stochastic processes related in the absence of Euclidean smooth structure? What new physical phenomena arise in the fractal-like settings that are ubiquitous in nature? This book introduces background and recent progress on these problems, from both established leaders in the field and early career researchers. The book gives a broad introduction to several foundational techniques in fractal mathematics, while also introducing some specific new and significant results of interest to experts, such as that waves have infinite propagation speed on fractals. It contains sufficient introductory material that it can be read by new researchers or researchers from other areas who want to learn about fractal methods and results"--Publisher's website.


High-Dimensional Probability

High-Dimensional Probability

Author: Roman Vershynin

Publisher: Cambridge University Press

Published: 2018-09-27

Total Pages: 299

ISBN-13: 1108415199

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An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.


Feynman-Kac Formulae

Feynman-Kac Formulae

Author: Pierre Del Moral

Publisher: Springer Science & Business Media

Published: 2004-03-30

Total Pages: 584

ISBN-13: 9780387202686

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This text takes readers in a clear and progressive format from simple to recent and advanced topics in pure and applied probability such as contraction and annealed properties of non-linear semi-groups, functional entropy inequalities, empirical process convergence, increasing propagations of chaos, central limit, and Berry Esseen type theorems as well as large deviation principles for strong topologies on path-distribution spaces. Topics also include a body of powerful branching and interacting particle methods.


Probability in Physics

Probability in Physics

Author: Yemima Ben-Menahem

Publisher: Springer Science & Business Media

Published: 2012-01-25

Total Pages: 325

ISBN-13: 3642213286

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What is the role and meaning of probability in physical theory, in particular in two of the most successful theories of our age, quantum physics and statistical mechanics? Laws once conceived as universal and deterministic, such as Newton‘s laws of motion, or the second law of thermodynamics, are replaced in these theories by inherently probabilistic laws. This collection of essays by some of the world‘s foremost experts presents an in-depth analysis of the meaning of probability in contemporary physics. Among the questions addressed are: How are probabilities defined? Are they objective or subjective? What is their explanatory value? What are the differences between quantum and classical probabilities? The result is an informative and thought-provoking book for the scientifically inquisitive.


Understanding Interactions in Complex Systems

Understanding Interactions in Complex Systems

Author: Stéphane Cordier

Publisher: Cambridge Scholars Publishing

Published: 2017-11-06

Total Pages: 405

ISBN-13: 1527505219

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Since human activities are embedded in interactions, they are at the very center of the modeling of any form of social life, shaping societies, groups and interpersonal relationships. All theories of social, cognitive and cultural life are thus associated with explicit or tacit models of the nature of interactions and relations. This book proposes a multifaceted exploration of the complex nature of interactions, and of the modeling of complex interactional systems. It shows that all disciplines can be enriched by exploring alternative paradigms in the modeling of interactions, and that if discipline-bound studies tend to underestimate the multi-dimensional nature of interactions, ignoring it is not an option. It will be of great interest for anyone involved in disciplines such as economics, geography, linguistics, communication studies, education sciences and sociology, and in fields such as the study of networks, interactional systems, relations between agents, and mathematical and computational modeling.


Gibbs Measures and Phase Transitions

Gibbs Measures and Phase Transitions

Author: Hans-Otto Georgii

Publisher: Walter de Gruyter

Published: 2011-05-31

Total Pages: 561

ISBN-13: 3110250322

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"This book is much more than an introduction to the subject of its title. It covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics and as an up to date reference in its chosen topics it is a work of outstanding scholarship. It is in fact one of the author's stated aims that this comprehensive monograph should serve both as an introductory text and as a reference for the expert. In its latter function it informs the reader about the state of the art in several directions. It is introductory in the sense that it does not assume any prior knowledge of statistical mechanics and is accessible to a general readership of mathematicians with a basic knowledge of measure theory and probability. As such it should contribute considerably to the further growth of the already lively interest in statistical mechanics on the part of probabilists and other mathematicians." Fredos Papangelou, Zentralblatt MATH The second edition has been extended by a new section on large deviations and some comments on the more recent developments in the area.