Random Walks Random Fields And Disordered Systems

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Random Walks, Random Fields, and Disordered Systems

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

Author : Anton Bovier,David Brydges,Amin Coja-Oghlan,Dmitry Ioffe,Gregory F. Lawler
Publisher : Springer
Page : 239 pages
File Size : 47,8 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.

Advances in Disordered Systems, Random Processes and Some Applications

Pierluigi Contucci,Cristian Giardinà
Advances in Disordered Systems Random Processes and Some Applications Book PDF

Author : Pierluigi Contucci,Cristian Giardinà
Publisher : Cambridge University Press
Page : 383 pages
File Size : 45,7 Mb
Release : 2016-12-15
Category : Science
ISBN : 9781107124103

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Advances in Disordered Systems, Random Processes and Some Applications by Pierluigi Contucci,Cristian Giardinà Pdf

This book offers a unified perspective on the study of complex systems with contributions written by leading scientists from various disciplines, including mathematics, physics, computer science, biology, economics and social science. It is written for researchers from a broad range of scientific fields with an interest in recent developments in complex systems.

Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory

Roberto Fernandez,Jürg Fröhlich,Alan D. Sokal
Random Walks Critical Phenomena and Triviality in Quantum Field Theory Book PDF

Author : Roberto Fernandez,Jürg Fröhlich,Alan D. Sokal
Publisher : Springer Science & Business Media
Page : 446 pages
File Size : 49,9 Mb
Release : 2013-03-14
Category : Science
ISBN : 9783662028667

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Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory by Roberto Fernandez,Jürg Fröhlich,Alan D. Sokal Pdf

Simple random walks - or equivalently, sums of independent random vari ables - have long been a standard topic of probability theory and mathemat ical physics. In the 1950s, non-Markovian random-walk models, such as the self-avoiding walk,were introduced into theoretical polymer physics, and gradu ally came to serve as a paradigm for the general theory of critical phenomena. In the past decade, random-walk expansions have evolved into an important tool for the rigorous analysis of critical phenomena in classical spin systems and of the continuum limit in quantum field theory. Among the results obtained by random-walk methods are the proof of triviality of the cp4 quantum field theo ryin space-time dimension d (::::) 4, and the proof of mean-field critical behavior for cp4 and Ising models in space dimension d (::::) 4. The principal goal of the present monograph is to present a detailed review of these developments. It is supplemented by a brief excursion to the theory of random surfaces and various applications thereof. This book has grown out of research carried out by the authors mainly from 1982 until the middle of 1985. Our original intention was to write a research paper. However, the writing of such a paper turned out to be a very slow process, partly because of our geographical separation, partly because each of us was involved in other projects that may have appeared more urgent.

Non-equilibrium Statistical Physics with Application to Disordered Systems

Manuel Osvaldo Cáceres
Non equilibrium Statistical Physics with Application to Disordered Systems Book PDF

Author : Manuel Osvaldo Cáceres
Publisher : Springer
Page : 556 pages
File Size : 50,6 Mb
Release : 2017-03-07
Category : Science
ISBN : 9783319515533

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Non-equilibrium Statistical Physics with Application to Disordered Systems by Manuel Osvaldo Cáceres Pdf

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.

Random Walks, Brownian Motion, and Interacting Particle Systems

H. Kesten,R. Durrett
Random Walks Brownian Motion and Interacting Particle Systems Book PDF

Author : H. Kesten,R. Durrett
Publisher : Springer Science & Business Media
Page : 457 pages
File Size : 42,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461204596

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Random Walks, Brownian Motion, and Interacting Particle Systems by H. Kesten,R. Durrett Pdf

This collection of articles is dedicated to Frank Spitzer on the occasion of his 65th birthday. The articles, written by a group of his friends, colleagues, former students and coauthors, are intended to demonstrate the major influence Frank has had on probability theory for the last 30 years and most likely will have for many years to come. Frank has always liked new phenomena, clean formulations and elegant proofs. He has created or opened up several research areas and it is not surprising that many people are still working out the consequences of his inventions. By way of introduction we have reprinted some of Frank's seminal articles so that the reader can easily see for himself the point of origin for much of the research presented here. These articles of Frank's deal with properties of Brownian motion, fluctuation theory and potential theory for random walks, and, of course, interacting particle systems. The last area was started by Frank as part of the general resurgence of treating problems of statistical mechanics with rigorous probabilistic tools.

Spin Glasses and Random Fields

A. Peter Young
Spin Glasses and Random Fields Book PDF

Author : A. Peter Young
Publisher : World Scientific
Page : 454 pages
File Size : 50,8 Mb
Release : 1998
Category : Science
ISBN : 9789810232405

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Spin Glasses and Random Fields by A. Peter Young Pdf

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.

Spin Glasses And Random Fields

Peter A Young
Spin Glasses And Random Fields Book PDF

Author : Peter A Young
Publisher : World Scientific
Page : 456 pages
File Size : 46,9 Mb
Release : 1997-12-23
Category : Science
ISBN : 9789814497268

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Spin Glasses And Random Fields by Peter A Young Pdf

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

Francis Comets
Directed Polymers in Random Environments Book PDF

Author : Francis Comets
Publisher : Springer
Page : 199 pages
File Size : 46,6 Mb
Release : 2017-01-26
Category : Mathematics
ISBN : 9783319504872

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Directed Polymers in Random Environments by Francis Comets Pdf

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.

Topics in Percolative and Disordered Systems

Alejandro F. Ramírez,Gérard Ben Arous,Pablo A. Ferrari,Charles M. Newman,Vladas Sidoravicius,Maria Eulália Vares
Topics in Percolative and Disordered Systems Book PDF

Author : Alejandro F. Ramírez,Gérard Ben Arous,Pablo A. Ferrari,Charles M. Newman,Vladas Sidoravicius,Maria Eulália Vares
Publisher : Springer
Page : 171 pages
File Size : 47,5 Mb
Release : 2014-06-16
Category : Mathematics
ISBN : 9781493903399

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Topics in Percolative and Disordered Systems by Alejandro F. Ramírez,Gérard Ben Arous,Pablo A. Ferrari,Charles M. Newman,Vladas Sidoravicius,Maria Eulália Vares Pdf

This volume features selected and peer-reviewed articles from the Pan-American Advanced Studies Institute (PASI). The chapters are written by international specialists who participated in the conference. Topics include developments based on breakthroughs in the mathematical understanding of phenomena describing systems in highly inhomogeneous and disordered media, including the KPZ universality class (describing the evolution of interfaces in two dimensions), random walks in random environment and percolative systems. PASI fosters a collaboration between North American and Latin American researchers and students. The conference that inspired this volume took place in January 2012 in both Santiago de Chile and Buenos Aires. Researchers and graduate students will find timely research in probability theory, statistical physics and related disciplines.

Encyclopedic Dictionary of Condensed Matter Physics

Charles P. Poole, Jr.
Encyclopedic Dictionary of Condensed Matter Physics Book PDF

Author : Charles P. Poole, Jr.
Publisher : Academic Press
Page : 1672 pages
File Size : 50,8 Mb
Release : 2004-03-11
Category : Science
ISBN : 9780080545233

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Encyclopedic Dictionary of Condensed Matter Physics by Charles P. Poole, Jr. Pdf

This volume is a translation and revision of the Original Russian version by Baryahktar. It covers all of the main fields involved in Condensed Matter Physics, such as crystallography, electrical properties, fluids, magnetism, material properties, optics, radiation, semiconductors, and superconductivity, as well as highlights of important related subjects such as quantum mechanics, spectroscopy, and statistical mechanics. Both theoretical and experimental aspects of condensed matter are covered in detail. The entries range from very short paragraphs on topics where definitions are needed, such as Bloch's law, clathrate compound, donor, domain, Kondo lattice, mean free path, and Wigner crystal, to long discussions of more general or more comprehensive topics such as antiferromagnetism, crystal lattice dynamics, dislocations, Fermi surface, Josephson effect, luminescence, magnetic films, phase transitions and semiconductors. The main theoretical approaches to Condensed Matter Physics are explained. There are several long tables on, for example, Bravais lattices, characteristics of magnetic materials, units of physical quantities, symmetry groups. The properties of the main elements of the periodic table are given. Numerous entries not covered by standard Solid State Physics texts o Self-similarity o The adiabatic approximation o Bistability Emphasis on materials not discussed in standard texts o Activated carborn o Austenite o Bainite o Calamitics o Carbine o Delat phase o Discotics o Gunier-Preston zones o Heterodesmic structures o Heusler Alloys o Stress and strain deviators o Vicalloy · Each entry is fully cross-referenced to help tracking down all aspects of a topic under investigation Highly illustrated to clarify many concepts

Gaussian Processes on Trees

Anton Bovier
Gaussian Processes on Trees Book PDF

Author : Anton Bovier
Publisher : Cambridge University Press
Page : 211 pages
File Size : 40,6 Mb
Release : 2017
Category : Mathematics
ISBN : 9781107160491

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Gaussian Processes on Trees by Anton Bovier Pdf

This book presents recent advances in branching Brownian motion from the perspective of extreme value theory and statistical physics, for graduates.

Genealogies of Interacting Particle Systems

Matthias Birkner,Rongfeng Sun,Jan M. Swart
Genealogies of Interacting Particle Systems Book PDF

Author : Matthias Birkner,Rongfeng Sun,Jan M. Swart
Publisher : World Scientific
Page : 363 pages
File Size : 41,7 Mb
Release : 2020
Category : Biomathematics
ISBN : 9789811206092

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Genealogies of Interacting Particle Systems by Matthias Birkner,Rongfeng Sun,Jan M. Swart Pdf

"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.

Probability Theory and Mathematical Statistics. Vol. 2

B. Grigelionis,Yu. V. Prohorov,V. V. Sazonov,V. Statulevičius
Probability Theory and Mathematical Statistics Vol 2 Book PDF

Author : B. Grigelionis,Yu. V. Prohorov,V. V. Sazonov,V. Statulevičius
Publisher : Walter de Gruyter GmbH & Co KG
Page : 624 pages
File Size : 54,9 Mb
Release : 2020-05-18
Category : Mathematics
ISBN : 9783112319024

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Probability Theory and Mathematical Statistics. Vol. 2 by B. Grigelionis,Yu. V. Prohorov,V. V. Sazonov,V. Statulevičius Pdf

No detailed description available for "PROB. TH. MATH. ST. ( GRIGELIONIS) VOL. 2 PROC.5/1989 E-BOOK".

Statistical Mechanics of Classical and Disordered Systems

Véronique Gayrard,Louis-Pierre Arguin,Nicola Kistler,Irina Kourkova
Statistical Mechanics of Classical and Disordered Systems Book PDF

Author : Véronique Gayrard,Louis-Pierre Arguin,Nicola Kistler,Irina Kourkova
Publisher : Springer Nature
Page : 279 pages
File Size : 50,7 Mb
Release : 2019-09-15
Category : Mathematics
ISBN : 9783030290771

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Statistical Mechanics of Classical and Disordered Systems by Véronique Gayrard,Louis-Pierre Arguin,Nicola Kistler,Irina Kourkova Pdf

These proceedings of the conference Advances in Statistical Mechanics, held in Marseille, France, August 2018, focus on fundamental issues of equilibrium and non-equilibrium dynamics for classical mechanical systems, as well as on open problems in statistical mechanics related to probability, mathematical physics, computer science, and biology. Statistical mechanics, as envisioned more than a century ago by Boltzmann, Maxwell and Gibbs, has recently undergone stunning twists and developments which have turned this old discipline into one of the most active areas of truly interdisciplinary and cutting-edge research. The contributions to this volume, with their rather unique blend of rigorous mathematics and applications, outline the state-of-the-art of this success story in key subject areas of equilibrium and non-equilibrium classical and quantum statistical mechanics of both disordered and non-disordered systems. Aimed at researchers in the broad field of applied modern probability theory, this book, and in particular the review articles, will also be of interest to graduate students looking for a gentle introduction to active topics of current research.

Random Fields

Erik Vanmarcke
Random Fields Book PDF

Author : Erik Vanmarcke
Publisher : World Scientific
Page : 363 pages
File Size : 52,8 Mb
Release : 2010
Category : Mathematics
ISBN : 9789812562975

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Random Fields by Erik Vanmarcke Pdf

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.?