Ten Lectures On Random Media

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Ten Lectures on Random Media

Erwin Bolthausen,Alain-Sol Sznitman
Ten Lectures on Random Media Book PDF

Author : Erwin Bolthausen,Alain-Sol Sznitman
Publisher : Birkhäuser
Page : 120 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034881593

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Ten Lectures on Random Media by Erwin Bolthausen,Alain-Sol Sznitman Pdf

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.

Random Walks on Disordered Media and their Scaling Limits

Takashi Kumagai
Random Walks on Disordered Media and their Scaling Limits Book PDF

Author : Takashi Kumagai
Publisher : Springer
Page : 147 pages
File Size : 42,6 Mb
Release : 2014-01-25
Category : Mathematics
ISBN : 9783319031521

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Random Walks on Disordered Media and their Scaling Limits by Takashi Kumagai Pdf

In these lecture notes, we will analyze the behavior of random walk on disordered media by means of both probabilistic and analytic methods, and will study the scaling limits. We will focus on the discrete potential theory and how the theory is effectively used in the analysis of disordered media. The first few chapters of the notes can be used as an introduction to discrete potential theory. Recently, there has been significant progress on the theory of random walk on disordered media such as fractals and random media. Random walk on a percolation cluster(‘the ant in the labyrinth’)is one of the typical examples. In 1986, H. Kesten showed the anomalous behavior of a random walk on a percolation cluster at critical probability. Partly motivated by this work, analysis and diffusion processes on fractals have been developed since the late eighties. As a result, various new methods have been produced to estimate heat kernels on disordered media. These developments are summarized in the notes.

Mathematical Statistical Physics

Anonim
Mathematical Statistical Physics Book PDF

Author : Anonim
Publisher : Elsevier
Page : 849 pages
File Size : 55,8 Mb
Release : 2006-06-27
Category : Science
ISBN : 9780080479231

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Mathematical Statistical Physics by Anonim Pdf

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

Random Polymer Models

Giambattista Giacomin
Random Polymer Models Book PDF

Author : Giambattista Giacomin
Publisher : Imperial College Press
Page : 259 pages
File Size : 44,9 Mb
Release : 2007
Category : Technology & Engineering
ISBN : 9781860947865

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Random Polymer Models by Giambattista Giacomin Pdf

This volume introduces readers to the world of disordered systems and to some of the remarkable probabilistic techniques developed in the field. The author explores in depth a class of directed polymer models to which much attention has been devoted in the last 25 years, in particular in the fields of physical and biological sciences. The models treated have been widely used in studying, for example, the phenomena of polymer pinning on a defect line, the behavior of copolymers in proximity to an interface between selective solvents and the DNA denaturation transition. In spite of the apparent heterogeneity of this list, in mathematical terms, a unified vision emerges. One is in fact dealing with the natural statistical mechanics systems built on classical renewal sequences by introducing one-body potentials. This volume is also a self-contained mathematical account of the state of the art for this class of statistical mechanics models.

Spin Glasses

Erwin Bolthausen,Anton Bovier
Spin Glasses Book PDF

Author : Erwin Bolthausen,Anton Bovier
Publisher : Springer
Page : 190 pages
File Size : 51,9 Mb
Release : 2007-01-11
Category : Science
ISBN : 9783540409083

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Spin Glasses by Erwin Bolthausen,Anton Bovier Pdf

This book serves as a concise introduction to the state-of-the-art of spin glass theory. The collection of review papers are written by leading experts in the field and cover the topic from a wide variety of angles. The book will be useful to both graduate students and young researchers, as well as to anyone curious to know what is going on in this exciting area of mathematical physics.

Correlated Random Systems: Five Different Methods

Véronique Gayrard,Nicola Kistler
Correlated Random Systems Five Different Methods Book PDF

Author : Véronique Gayrard,Nicola Kistler
Publisher : Springer
Page : 208 pages
File Size : 55,5 Mb
Release : 2015-06-09
Category : Mathematics
ISBN : 9783319176741

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Correlated Random Systems: Five Different Methods by Véronique Gayrard,Nicola Kistler Pdf

This volume presents five different methods recently developed to tackle the large scale behavior of highly correlated random systems, such as spin glasses, random polymers, local times and loop soups and random matrices. These methods, presented in a series of lectures delivered within the Jean-Morlet initiative (Spring 2013), play a fundamental role in the current development of probability theory and statistical mechanics. The lectures were: Random Polymers by E. Bolthausen, Spontaneous Replica Symmetry Breaking and Interpolation Methods by F. Guerra, Derrida's Random Energy Models by N. Kistler, Isomorphism Theorems by J. Rosen and Spectral Properties of Wigner Matrices by B. Schlein. This book is the first in a co-edition between the Jean-Morlet Chair at CIRM and the Springer Lecture Notes in Mathematics which aims to collect together courses and lectures on cutting-edge subjects given during the term of the Jean-Morlet Chair, as well as new material produced in its wake. It is targeted at researchers, in particular PhD students and postdocs, working in probability theory and statistical physics.

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 : 178 pages
File Size : 41,9 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.

Effective Dynamics of Stochastic Partial Differential Equations

Jinqiao Duan,Wei Wang
Effective Dynamics of Stochastic Partial Differential Equations Book PDF

Author : Jinqiao Duan,Wei Wang
Publisher : Elsevier
Page : 283 pages
File Size : 54,8 Mb
Release : 2014-03-06
Category : Mathematics
ISBN : 9780128012697

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Effective Dynamics of Stochastic Partial Differential Equations by Jinqiao Duan,Wei Wang Pdf

Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations. The authors’ experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension. New techniques for extracting effective dynamics of infinite dimensional dynamical systems under uncertainty Accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations Solutions or hints to all Exercises

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 : 47,6 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.

In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius

Maria Eulália Vares,Roberto Fernández,Luiz Renato Fontes,Charles M. Newman
In and Out of Equilibrium 3 Celebrating Vladas Sidoravicius Book PDF

Author : Maria Eulália Vares,Roberto Fernández,Luiz Renato Fontes,Charles M. Newman
Publisher : Springer Nature
Page : 819 pages
File Size : 55,6 Mb
Release : 2021-03-25
Category : Mathematics
ISBN : 9783030607548

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In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius by Maria Eulália Vares,Roberto Fernández,Luiz Renato Fontes,Charles M. Newman Pdf

This is a volume in memory of Vladas Sidoravicius who passed away in 2019. Vladas has edited two volumes appeared in this series ("In and Out of Equilibrium") and is now honored by friends and colleagues with research papers reflecting Vladas' interests and contributions to probability theory.

Statistical Mechanics of Disordered Systems

Anton Bovier
Statistical Mechanics of Disordered Systems Book PDF

Author : Anton Bovier
Publisher : Cambridge University Press
Page : 297 pages
File Size : 50,5 Mb
Release : 2006-06-08
Category : Mathematics
ISBN : 9780521849913

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Statistical Mechanics of Disordered Systems by Anton Bovier Pdf

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Disorder and Critical Phenomena Through Basic Probability Models

Giambattista Giacomin
Disorder and Critical Phenomena Through Basic Probability Models Book PDF

Author : Giambattista Giacomin
Publisher : Springer Science & Business Media
Page : 140 pages
File Size : 45,6 Mb
Release : 2011-07-16
Category : Language Arts & Disciplines
ISBN : 9783642211553

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Disorder and Critical Phenomena Through Basic Probability Models by Giambattista Giacomin Pdf

Understanding the effect of disorder on critical phenomena is a central issue in statistical mechanics. In probabilistic terms: what happens if we perturb a system exhibiting a phase transition by introducing a random environment? The physics community has approached this very broad question by aiming at general criteria that tell whether or not the addition of disorder changes the critical properties of a model: some of the predictions are truly striking and mathematically challenging. We approach this domain of ideas by focusing on a specific class of models, the "pinning models," for which a series of recent mathematical works has essentially put all the main predictions of the physics community on firm footing; in some cases, mathematicians have even gone beyond, settling a number of controversial issues. But the purpose of these notes, beyond treating the pinning models in full detail, is also to convey the gist, or at least the flavor, of the "overall picture," which is, in many respects, unfamiliar territory for mathematicians.

The Mathematics of the Bose Gas and its Condensation

Elliott H. Lieb,Robert Seiringer,Jan Philip Solovej,Jakob Yngvason
The Mathematics of the Bose Gas and its Condensation Book PDF

Author : Elliott H. Lieb,Robert Seiringer,Jan Philip Solovej,Jakob Yngvason
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 48,8 Mb
Release : 2005-06-16
Category : Science
ISBN : 3764373369

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The Mathematics of the Bose Gas and its Condensation by Elliott H. Lieb,Robert Seiringer,Jan Philip Solovej,Jakob Yngvason Pdf

This book contains a unique survey of the mathematically rigorous results about the quantum-mechanical many-body problem that have been obtained by the authors in the past seven years. It addresses a topic that is not only rich mathematically, using a large variety of techniques in mathematical analysis, but is also one with strong ties to current experiments on ultra-cold Bose gases and Bose-Einstein condensation. The book provides a pedagogical entry into an active area of ongoing research for both graduate students and researchers. It is an outgrowth of a course given by the authors for graduate students and post-doctoral researchers at the Oberwolfach Research Institute in 2004. The book also provides a coherent summary of the field and a reference for mathematicians and physicists active in research on quantum mechanics.

Lectures on Probability Theory and Statistics

Evarist Giné,Geoffrey R. Grimmett,Laurent Saloff-Coste
Lectures on Probability Theory and Statistics Book PDF

Author : Evarist Giné,Geoffrey R. Grimmett,Laurent Saloff-Coste
Publisher : Springer
Page : 431 pages
File Size : 41,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540692102

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Lectures on Probability Theory and Statistics by Evarist Giné,Geoffrey R. Grimmett,Laurent Saloff-Coste Pdf

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Percolation

Geoffrey R. Grimmett
Percolation Book PDF

Author : Geoffrey R. Grimmett
Publisher : Springer Science & Business Media
Page : 459 pages
File Size : 48,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662039816

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Percolation by Geoffrey R. Grimmett Pdf

Percolation theory is the study of an idealized random medium in two or more dimensions. The emphasis of this book is upon core mathematical material and the presentation of the shortest and most accessible proofs. Much new material appears in this second edition including dynamic and static renormalization, strict inequalities between critical points, a sketch of the lace expansion, and several essays on related fields and applications.