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Conformal Invariance An Introduction To Loops Interfaces And Stochastic Loewner Evolution
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Book Synopsis Conformal Invariance: an Introduction to Loops, Interfaces and Stochastic Loewner Evolution by : Malte Henkel
Download or read book Conformal Invariance: an Introduction to Loops, Interfaces and Stochastic Loewner Evolution written by Malte Henkel and published by Springer Science & Business Media. This book was released on 2012-04-05 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conformal invariance has been a spectacularly successful tool in advancing our understanding of the two-dimensional phase transitions found in classical systems at equilibrium. This volume sharpens our picture of the applications of conformal invariance, introducing non-local observables such as loops and interfaces before explaining how they arise in specific physical contexts. It then shows how to use conformal invariance to determine their properties. Moving on to cover key conceptual developments in conformal invariance, the book devotes much of its space to stochastic Loewner evolution (SLE), detailing SLE’s conceptual foundations as well as extensive numerical tests. The chapters then elucidate SLE’s use in geometric phase transitions such as percolation or polymer systems, paying particular attention to surface effects. As clear and accessible as it is authoritative, this publication is as suitable for non-specialist readers and graduate students alike.
Download or read book Conformal Invariance written by and published by Springer. This book was released on 2012-04-06 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Conformal Invariance: an Introduction to Loops, Interfaces and Stochastic Loewner Evolution by : Malte Henkel
Download or read book Conformal Invariance: an Introduction to Loops, Interfaces and Stochastic Loewner Evolution written by Malte Henkel and published by Springer Science & Business Media. This book was released on 2012-04-04 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conformal invariance has been a spectacularly successful tool in advancing our understanding of the two-dimensional phase transitions found in classical systems at equilibrium. This volume sharpens our picture of the applications of conformal invariance, introducing non-local observables such as loops and interfaces before explaining how they arise in specific physical contexts. It then shows how to use conformal invariance to determine their properties. Moving on to cover key conceptual developments in conformal invariance, the book devotes much of its space to stochastic Loewner evolution (SLE), detailing SLE’s conceptual foundations as well as extensive numerical tests. The chapters then elucidate SLE’s use in geometric phase transitions such as percolation or polymer systems, paying particular attention to surface effects. As clear and accessible as it is authoritative, this publication is as suitable for non-specialist readers and graduate students alike.
Book Synopsis Probability, Geometry and Integrable Systems by : Mark Pinsky
Download or read book Probability, Geometry and Integrable Systems written by Mark Pinsky and published by Cambridge University Press. This book was released on 2008-03-17 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reflects the range of mathematical interests of Henry McKean, to whom it is dedicated.
Book Synopsis Random Walks and Geometry by : Vadim Kaimanovich
Download or read book Random Walks and Geometry written by Vadim Kaimanovich and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Die jüngsten Entwicklungen zeigen, dass sich Wahrscheinlichkeitsverfahren zu einem sehr wirkungsvollen Werkzeug entwickelt haben, und das auf so unterschiedlichen Gebieten wie statistische Physik, dynamische Systeme, Riemann'sche Geometrie, Gruppentheorie, harmonische Analyse, Graphentheorie und Informatik.
Book Synopsis Schramm–Loewner Evolution by : Antti Kemppainen
Download or read book Schramm–Loewner Evolution written by Antti Kemppainen and published by Springer. This book was released on 2017-12-22 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a short, but complete, introduction to the Loewner equation and the SLEs, which are a family of random fractal curves, as well as the relevant background in probability and complex analysis. The connection to statistical physics is also developed in the text in an example case. The book is based on a course (with the same title) lectured by the author. First three chapters are devoted to the background material, but at the same time, give the reader a good understanding on the overview on the subject and on some aspects of conformal invariance. The chapter on the Loewner equation develops in detail the connection of growing hulls and the differential equation satisfied by families of conformal maps. The Schramm–Loewner evolutions are defined and their basic properties are studied in the following chapter, and the regularity properties of random curves as well as scaling limits of discrete random curves are investigated in the final chapter. The book is aimed at graduate students or researchers who want to learn the subject fairly quickly.
Book Synopsis Conformally Invariant Processes in the Plane by : Gregory F. Lawler
Download or read book Conformally Invariant Processes in the Plane written by Gregory F. Lawler and published by American Mathematical Soc.. This book was released on 2008 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an introduction to the conformally invariant processes that appear as scaling limits. This book covers such topics as stochastic integration, and complex Brownian motion and measures derived from Brownian motion. It is suitable for those interested in random processes and their applications in theoretical physics.
Book Synopsis Selected Works of Oded Schramm by : Itai Benjamini
Download or read book Selected Works of Oded Schramm written by Itai Benjamini and published by Springer Science & Business Media. This book was released on 2011-08-12 with total page 1199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the memory of the late Oded Schramm (1961-2008), distinguished mathematician. Throughout his career, Schramm made profound and beautiful contributions to mathematics that will have a lasting influence. In these two volumes, Editors Itai Benjamini and Olle Häggström have collected some of his papers, supplemented with three survey papers by Steffen Rohde, Häggström and Cristophe Garban that further elucidate his work. The papers within are a representative collection that shows the breadth, depth, enthusiasm and clarity of his work, with sections on Geometry, Noise Sensitivity, Random Walks and Graph Limits, Percolation, and finally Schramm-Loewner Evolution. An introduction by the Editors and a comprehensive bibliography of Schramm's publications complete the volume. The book will be of especial interest to researchers in probability and geometry, and in the history of these subjects.
Author :Clay Mathematics Institute. Summer School Publisher :American Mathematical Soc. ISBN 13 :0821868632 Total Pages :481 pages Book Rating :4.8/5 (218 download)
Book Synopsis Probability and Statistical Physics in Two and More Dimensions by : Clay Mathematics Institute. Summer School
Download or read book Probability and Statistical Physics in Two and More Dimensions written by Clay Mathematics Institute. Summer School and published by American Mathematical Soc.. This book was released on 2012 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of lecture notes for six of the ten courses given in Buzios, Brazil by prominent probabilists at the 2010 Clay Mathematics Institute Summer School, ``Probability and Statistical Physics in Two and More Dimensions'' and at the XIV Brazilian School of Probability. In the past ten to fifteen years, various areas of probability theory related to statistical physics, disordered systems and combinatorics have undergone intensive development. A number of these developments deal with two-dimensional random structures at their critical points, and provide new tools and ways of coping with at least some of the limitations of Conformal Field Theory that had been so successfully developed in the theoretical physics community to understand phase transitions of two-dimensional systems. Included in this selection are detailed accounts of all three foundational courses presented at the Clay school--Schramm-Loewner Evolution and other Conformally Invariant Objects, Noise Sensitivity and Percolation, Scaling Limits of Random Trees and Planar Maps--together with contributions on Fractal and Multifractal properties of SLE and Conformal Invariance of Lattice Models. Finally, the volume concludes with extended articles based on the courses on Random Polymers and Self-Avoiding Walks given at the Brazilian School of Probability during the final week of the school. Together, these notes provide a panoramic, state-of-the-art view of probability theory areas related to statistical physics, disordered systems and combinatorics. Like the lectures themselves, they are oriented towards advanced students and postdocs, but experts should also find much of interest.
Book Synopsis Probability on Graphs by : Geoffrey Grimmett
Download or read book Probability on Graphs written by Geoffrey Grimmett and published by Cambridge University Press. This book was released on 2018-01-25 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
Book Synopsis Markov Processes and Related Fields by :
Download or read book Markov Processes and Related Fields written by and published by . This book was released on 2007 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Non-Equilibrium Entropy and Irreversibility by : C. Lindblad
Download or read book Non-Equilibrium Entropy and Irreversibility written by C. Lindblad and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of deriving irreversible thermodynamics from the re versible microscopic dynamics has been on the agenda of theoreti cal physics for a century and has produced more papers than can be digested by any single scientist. Why add to this too long list with yet another work? The goal is definitely not to give a gen eral review of previous work in this field. My ambition is rather to present an approach differing in some key aspects from the stan dard treatments, and to develop it as far as possible using rather simple mathematical tools (mainly inequalities of various kinds). However, in the course of this work I have used a large number of results and ideas from the existing literature, and the reference list contains contributions from many different lines of research. As a consequence the reader may find the arguments a bit difficult to follow without some previous exposure to this set of problems.
Book Synopsis The Random-Cluster Model by : Geoffrey R. Grimmett
Download or read book The Random-Cluster Model written by Geoffrey R. Grimmett and published by Springer Science & Business Media. This book was released on 2006-12-13 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The random-cluster model has emerged as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems. The book includes treatment of the first-order (discontinuous) phase transition.
Book Synopsis Noise Sensitivity of Boolean Functions and Percolation by : Christophe Garban
Download or read book Noise Sensitivity of Boolean Functions and Percolation written by Christophe Garban and published by Cambridge University Press. This book was released on 2015 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to cover the theory of noise sensitivity of Boolean functions with particular emphasis on critical percolation.
Book Synopsis Random Surfaces by : Scott Sheffield
Download or read book Random Surfaces written by Scott Sheffield and published by . This book was released on 2005 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Percolation Theory for Mathematicians by : Kesten
Download or read book Percolation Theory for Mathematicians written by Kesten and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quite apart from the fact that percolation theory had its orlgln in an honest applied problem (see Hammersley and Welsh (1980)), it is a source of fascinating problems of the best kind a mathematician can wish for: problems which are easy to state with a minimum of preparation, but whose solutions are (apparently) difficult and require new methods. At the same time many of the problems are of interest to or proposed by statistical physicists and not dreamt up merely to demons~te ingenuity. Progress in the field has been slow. Relatively few results have been established rigorously, despite the rapidly growing literature with variations and extensions of the basic model, conjectures, plausibility arguments and results of simulations. It is my aim to treat here some basic results with rigorous proofs. This is in the first place a research monograph, but there are few prerequisites; one term of any standard graduate course in probability should be more than enough. Much of the material is quite recent or new, and many of the proofs are still clumsy. Especially the attempt to give proofs valid for as many graphs as possible led to more complications than expected. I hope that the Applications and Examples provide justifi cation for going to this level of generality.
Book Synopsis The Self-Avoiding Walk by : Neal Madras
Download or read book The Self-Avoiding Walk written by Neal Madras and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-avoiding walk is a path on a lattice that does not visit the same site more than once. In spite of this simple definition, many of the most basic questions about this model are difficult to resolve in a mathematically rigorous fashion. In particular, we do not know much about how far an n step self-avoiding walk typically travels from its starting point, or even how many such walks there are. These and other important questions about the self-avoiding walk remain unsolved in the rigorous mathematical sense, although the physics and chemistry communities have reached consensus on the answers by a variety of nonrigorous methods, including computer simulations. But there has been progress among mathematicians as well, much of it in the last decade, and the primary goal of this book is to give an account of the current state of the art as far as rigorous results are concerned. A second goal of this book is to discuss some of the applications of the self-avoiding walk in physics and chemistry, and to describe some of the nonrigorous methods used in those fields. The model originated in chem istry several decades ago as a model for long-chain polymer molecules. Since then it has become an important model in statistical physics, as it exhibits critical behaviour analogous to that occurring in the Ising model and related systems such as percolation.
