Random Walks Random Fields And Disordered Systems
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Random Walks Random Fields And Disordered Systems
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Author : Anton Bovier
language : en
Publisher: Springer
Release Date : 2015-09-21
Random Walks Random Fields And Disordered Systems written by Anton Bovier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-21 with Science categories.
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.
Spin Glasses And Random Fields
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Author : A. Peter Young
language : en
Publisher: World Scientific
Release Date : 1998
Spin Glasses And Random Fields written by A. Peter Young and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Science categories.
The last few years have seen many developments in the study of ?frustrated? systems, such as spin glasses and random fields. In addition, the application of the idea of spin glasses to other branches of physics, such as vortex lines in high temperature superconductors, protein folding, structural glasses, and the vulcanization of rubber, has been flourishing. The earlier reviews are several years old, so now is an appropriate time to summarize the recent developments. The articles in this book have been written by leading researchers and include theoretical and experimental studies, and large-scale numerical work (using state-of-the-art algorithms designed specifically for spin-glass-type problems), as well as analytical studies.
Directed Polymers In Random Environments
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Author : Francis Comets
language : en
Publisher: Springer
Release Date : 2017-01-26
Directed Polymers In Random Environments written by Francis Comets and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-26 with Mathematics categories.
Analyzing the phase transition from diffusive to localized behavior in a model of directed polymers in a random environment, this volume places particular emphasis on the localization phenomenon. The main questionis: What does the path of a random walk look like if rewards and penalties are spatially randomly distributed?This model, which provides a simplified version of stretched elastic chains pinned by random impurities, has attracted much research activity, but it (and its relatives) still holds many secrets, especially in high dimensions. It has non-gaussian scaling limits and it belongs to the so-called KPZ universality class when the space is one-dimensional. Adopting a Gibbsian approach, using general and powerful tools from probability theory, the discrete model is studied in full generality. Presenting the state-of-the art from different perspectives, and written in the form of a first course on the subject, this monograph is aimed at researchers in probability or statistical physics, but is also accessible to masters and Ph.D. students.
Random Fields Analysis And Synthesis Revised And Expanded New Edition
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Author : Erik Vanmarcke
language : en
Publisher: World Scientific Publishing Company
Release Date : 2010-07-21
Random Fields Analysis And Synthesis Revised And Expanded New Edition written by Erik Vanmarcke and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-21 with Mathematics categories.
Random variation is a fact of life that provides substance to a wide range of problems in the sciences, engineering, and economics. There is a growing need in diverse disciplines to model complex patterns of variation and interdependence using random fields, as both deterministic treatment and conventional statistics are often insufficient. An ideal random field model will capture key features of complex random phenomena in terms of a minimum number of physically meaningful and experimentally accessible parameters. This volume, a revised and expanded edition of an acclaimed book first published by the M I T Press, offers a synthesis of methods to describe and analyze and, where appropriate, predict and control random fields. There is much new material, covering both theory and applications, notably on a class of probability distributions derived from quantum mechanics, relevant to stochastic modeling in fields such as cosmology, biology and system reliability, and on discrete-unit or agent-based random processes.Random Fields is self-contained and unified in presentation. The first edition was found, in a review in EOS (American Geophysical Union) to be “both technically interesting and a pleasure to read … the presentation is clear and the book should be useful to almost anyone who uses random processes to solve problems in engineering or science … and (there is) continued emphasis on describing the mathematics in physical terms.”
Non Equilibrium Statistical Physics With Application To Disordered Systems
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Author : Manuel Osvaldo Cáceres
language : en
Publisher: Springer
Release Date : 2017-03-07
Non Equilibrium Statistical Physics With Application To Disordered Systems written by Manuel Osvaldo Cáceres and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-07 with Science categories.
This textbook is the result of the enhancement of several courses on non-equilibrium statistics, stochastic processes, stochastic differential equations, anomalous diffusion and disorder. The target audience includes students of physics, mathematics, biology, chemistry, and engineering at undergraduate and graduate level with a grasp of the basic elements of mathematics and physics of the fourth year of a typical undergraduate course. The little-known physical and mathematical concepts are described in sections and specific exercises throughout the text, as well as in appendices. Physical-mathematical motivation is the main driving force for the development of this text. It presents the academic topics of probability theory and stochastic processes as well as new educational aspects in the presentation of non-equilibrium statistical theory and stochastic differential equations.. In particular it discusses the problem of irreversibility in that context and the dynamics of Fokker-Planck. An introduction on fluctuations around metastable and unstable points are given. It also describes relaxation theory of non-stationary Markov periodic in time systems. The theory of finite and infinite transport in disordered networks, with a discussion of the issue of anomalous diffusion is introduced. Further, it provides the basis for establishing the relationship between quantum aspects of the theory of linear response and the calculation of diffusion coefficients in amorphous systems.
Probability Theory And Mathematical Statistics Vol 2
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Author : B. Grigelionis
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-05-18
Probability Theory And Mathematical Statistics Vol 2 written by B. Grigelionis and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-18 with Mathematics categories.
No detailed description available for "PROB. TH. MATH. ST. ( GRIGELIONIS) VOL. 2 PROC.5/1989 E-BOOK".
Genealogies Of Interacting Particle Systems
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Author : Matthias Birkner
language : en
Publisher: World Scientific
Release Date : 2020
Genealogies Of Interacting Particle Systems written by Matthias Birkner and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Biomathematics categories.
"Interacting particle systems are Markov processes involving infinitely many interacting components. Since their introduction in the 1970s, researchers have found many applications in statistical physics and population biology. Genealogies, which follow the origin of the state of a site backwards in time, play an important role in their studies, especially for the biologically motivated systems. The program Genealogies of Interacting Particle Systems held at the Institute for Mathematical Sciences, National University of Singapore, from 17 July to 18 Aug 2017, brought together experts and young researchers interested in this modern topic. Central to the program were learning sessions where lecturers presented work outside of their own research, as well as a normal workshop "--Publisher's website.
Random Graphs Phase Transitions And The Gaussian Free Field
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Author : Martin T. Barlow
language : en
Publisher: Springer Nature
Release Date : 2019-12-03
Random Graphs Phase Transitions And The Gaussian Free Field written by Martin T. Barlow and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-03 with Mathematics categories.
The 2017 PIMS-CRM Summer School in Probability was held at the Pacific Institute for the Mathematical Sciences (PIMS) at the University of British Columbia in Vancouver, Canada, during June 5-30, 2017. It had 125 participants from 20 different countries, and featured two main courses, three mini-courses, and twenty-nine lectures. The lecture notes contained in this volume provide introductory accounts of three of the most active and fascinating areas of research in modern probability theory, especially designed for graduate students entering research: Scaling limits of random trees and random graphs (Christina Goldschmidt) Lectures on the Ising and Potts models on the hypercubic lattice (Hugo Duminil-Copin) Extrema of the two-dimensional discrete Gaussian free field (Marek Biskup) Each of these contributions provides a thorough introduction that will be of value to beginners and experts alike.
Gaussian Processes On Trees
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Author : Anton Bovier
language : en
Publisher: Cambridge University Press
Release Date : 2017
Gaussian Processes On Trees written by Anton Bovier and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.
This book presents recent advances in branching Brownian motion from the perspective of extreme value theory and statistical physics, for graduates.
An Unbounded Experience In Random Walks With Applications
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Author : Michael F Shlesinger
language : en
Publisher: World Scientific
Release Date : 2021-06-29
An Unbounded Experience In Random Walks With Applications written by Michael F Shlesinger and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-29 with Mathematics categories.
This volume comprises the author's account of the development of novel results in random walk theory and its applications during the fractal and chaos revolutions. The early history of probability is presented in an engaging manner, and peppered with pitfalls and paradoxes. Readers will find the introduction of Paul Lévy's work via Mandelbrot's Lévy flights which are featured uniquely as Weierstrass and Riemann random walks.Generalizations to coupled memories, internal states and fractal time are introduced at the level for graduate students. Mathematical developments are explained including Green's functions, inverse Mellin transforms, Jacobians, and matrix methods. Applications are made to anomalous diffusion and conductivity in amorphous semiconductors and supercooled liquids. The glass transition is discussed especially for pressure effects.All along the way, personal stories are recounted and special appreciations are made to Elliott Montroll and Harvey Scher for their ever-expanding influence on the field of non-equilibrium anomalous processes that now are found in topics including disordered materials, water table processes, animal foraging, blinking quantum dots, rotating flows, optical lattices, dynamical strange attractors and strange kinetics.