Lecture Notes On The Gaussian Free Field

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Random Graphs, Phase Transitions, and the Gaussian Free Field

Author : Martin T. Barlow
Publisher : Springer Nature
ISBN 13 : 3030320111
Total Pages : 421 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Random Graphs, Phase Transitions, and the Gaussian Free Field by : Martin T. Barlow

Download or read book Random Graphs, Phase Transitions, and the Gaussian Free Field written by Martin T. Barlow and published by Springer Nature. This book was released on 2019-12-03 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Random Surfaces

Author : Scott Sheffield
Publisher :
ISBN 13 :
Total Pages : 194 pages
Book Rating : 4.F/5 ( download)

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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:

Topics in Occupation Times and Gaussian Free Fields

Author : Alain-Sol Sznitman
Publisher : European Mathematical Society
ISBN 13 : 9783037191095
Total Pages : 128 pages
Book Rating : 4.1/5 (91 download)

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Book Synopsis Topics in Occupation Times and Gaussian Free Fields by : Alain-Sol Sznitman

Download or read book Topics in Occupation Times and Gaussian Free Fields written by Alain-Sol Sznitman and published by European Mathematical Society. This book was released on 2012 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of a graduate course at ETH Zurich during the spring 2011 term. It explores various links between such notions as occupation times of Markov chains, Gaussian free fields, Poisson point processes of Markovian loops, and random interlacements, which have been the object of intensive research over the last few years. These notions are developed in the convenient setup of finite weighted graphs endowed with killing measures. This book first discusses elements of continuous-time Markov chains, Dirichlet forms, potential theory, together with some consequences for Gaussian free fields. Next, isomorphism theorems and generalized Ray-Knight theorems, which relate occupation times of Markov chains to Gaussian free fields, are presented. Markovian loops are constructed and some of their key properties derived. The field of occupation times of Poisson point processes of Markovian loops is investigated. Of special interest are its connection to the Gaussian free field, and a formula of Symanzik. Finally, links between random interlacements and Markovian loops are discussed, and some further connections with Gaussian free fields are mentioned.

Statistical Mechanics of Lattice Systems

Author : Sacha Friedli
Publisher : Cambridge University Press
ISBN 13 : 1107184827
Total Pages : 643 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Statistical Mechanics of Lattice Systems by : Sacha Friedli

Download or read book Statistical Mechanics of Lattice Systems written by Sacha Friedli and published by Cambridge University Press. This book was released on 2017-11-23 with total page 643 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.

Lectures on Random Lozenge Tilings

Author : Vadim Gorin
Publisher : Cambridge University Press
ISBN 13 : 1108922902
Total Pages : 262 pages
Book Rating : 4.1/5 (89 download)

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Book Synopsis Lectures on Random Lozenge Tilings by : Vadim Gorin

Download or read book Lectures on Random Lozenge Tilings written by Vadim Gorin and published by Cambridge University Press. This book was released on 2021-09-09 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past 25 years, there has been an explosion of interest in the area of random tilings. The first book devoted to the topic, this timely text describes the mathematical theory of tilings. It starts from the most basic questions (which planar domains are tileable?), before discussing advanced topics about the local structure of very large random tessellations. The author explains each feature of random tilings of large domains, discussing several different points of view and leading on to open problems in the field. The book is based on upper-division courses taught to a variety of students but it also serves as a self-contained introduction to the subject. Test your understanding with the exercises provided and discover connections to a wide variety of research areas in mathematics, theoretical physics, and computer science, such as conformal invariance, determinantal point processes, Gibbs measures, high-dimensional random sampling, symmetric functions, and variational problems.

Lectures on Field Theory and Topology

Author : Daniel S. Freed
Publisher : American Mathematical Soc.
ISBN 13 : 1470452065
Total Pages : 202 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Lectures on Field Theory and Topology by : Daniel S. Freed

Download or read book Lectures on Field Theory and Topology written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 2019-08-23 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.

Lecture Notes On Field Theory In Condensed Matter Physics

Author : Christopher Mudry
Publisher : World Scientific Publishing Company
ISBN 13 : 9814449121
Total Pages : 745 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Lecture Notes On Field Theory In Condensed Matter Physics by : Christopher Mudry

Download or read book Lecture Notes On Field Theory In Condensed Matter Physics written by Christopher Mudry and published by World Scientific Publishing Company. This book was released on 2014-02-28 with total page 745 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to introduce a graduate student to selected concepts in condensed matter physics for which the language of field theory is ideally suited. The examples considered in this book are those of superfluidity for weakly interacting bosons, collinear magnetism, and superconductivity. Quantum phase transitions are also treated in the context of quantum dissipative junctions and interacting fermions constrained to one-dimensional position space. The style of presentation is sufficiently detailed and comprehensive that it only presumes familiarity with undergraduate physics.

Complex Analysis and Dynamical Systems

Author : Mark Agranovsky
Publisher : Birkhäuser
ISBN 13 : 3319701541
Total Pages : 373 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Complex Analysis and Dynamical Systems by : Mark Agranovsky

Download or read book Complex Analysis and Dynamical Systems written by Mark Agranovsky and published by Birkhäuser. This book was released on 2018-01-31 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on developments in complex dynamical systems and geometric function theory over the past decade, showing strong links with other areas of mathematics and the natural sciences. Traditional methods and approaches surface in physics and in the life and engineering sciences with increasing frequency – the Schramm‐Loewner evolution, Laplacian growth, and quadratic differentials are just a few typical examples. This book provides a representative overview of these processes and collects open problems in the various areas, while at the same time showing where and how each particular topic evolves. This volume is dedicated to the memory of Alexander Vasiliev.

Stochastic Processes and Random Matrices

Author : Gregory Schehr
Publisher : Oxford University Press
ISBN 13 : 0198797311
Total Pages : 641 pages
Book Rating : 4.1/5 (987 download)

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Book Synopsis Stochastic Processes and Random Matrices by : Gregory Schehr

Download or read book Stochastic Processes and Random Matrices written by Gregory Schehr and published by Oxford University Press. This book was released on 2017 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text covers in detail recent developments in the field of stochastic processes and Random Matrix Theory. Matrix models have been playing an important role in theoretical physics for a long time and are currently also a very active domain of research in mathematics.

Random Walks and Physical Fields

Author : Yves Le Jan
Publisher : Springer Nature
ISBN 13 : 3031579232
Total Pages : 188 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis Random Walks and Physical Fields by : Yves Le Jan

Download or read book Random Walks and Physical Fields written by Yves Le Jan and published by Springer Nature. This book was released on with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Gaussian Processes on Trees

Author : Anton Bovier
Publisher : Cambridge University Press
ISBN 13 : 1107160499
Total Pages : 211 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Gaussian Processes on Trees by : Anton Bovier

Download or read book Gaussian Processes on Trees written by Anton Bovier and published by Cambridge University Press. This book was released on 2017 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent advances in branching Brownian motion from the perspective of extreme value theory and statistical physics, for graduates.

Percolation on Triangulations: A Bijective Path to Liouville Quantum Gravity

Author : Olivier Bernardi
Publisher : American Mathematical Society
ISBN 13 : 1470466996
Total Pages : 188 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Percolation on Triangulations: A Bijective Path to Liouville Quantum Gravity by : Olivier Bernardi

Download or read book Percolation on Triangulations: A Bijective Path to Liouville Quantum Gravity written by Olivier Bernardi and published by American Mathematical Society. This book was released on 2023-09-27 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Markov Paths, Loops and Fields

Author : Yves Le Jan
Publisher : Springer Science & Business Media
ISBN 13 : 3642212158
Total Pages : 128 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Markov Paths, Loops and Fields by : Yves Le Jan

Download or read book Markov Paths, Loops and Fields written by Yves Le Jan and published by Springer Science & Business Media. This book was released on 2011-07-06 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of these notes is to explore some simple relations between Markovian path and loop measures, the Poissonian ensembles of loops they determine, their occupation fields, uniform spanning trees, determinants, and Gaussian Markov fields such as the free field. These relations are first studied in complete generality for the finite discrete setting, then partly generalized to specific examples in infinite and continuous spaces.

Introduction to a Renormalisation Group Method

Author : Roland Bauerschmidt
Publisher : Springer Nature
ISBN 13 : 9813295937
Total Pages : 283 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Introduction to a Renormalisation Group Method by : Roland Bauerschmidt

Download or read book Introduction to a Renormalisation Group Method written by Roland Bauerschmidt and published by Springer Nature. This book was released on 2019-10-16 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a primer on a mathematically rigorous renormalisation group theory, presenting mathematical techniques fundamental to renormalisation group analysis such as Gaussian integration, perturbative renormalisation and the stable manifold theorem. It also provides an overview of fundamental models in statistical mechanics with critical behaviour, including the Ising and φ4 models and the self-avoiding walk. The book begins with critical behaviour and its basic discussion in statistical mechanics models, and subsequently explores perturbative and non-perturbative analysis in the renormalisation group. Lastly it discusses the relation of these topics to the self-avoiding walk and supersymmetry. Including exercises in each chapter to help readers deepen their understanding, it is a valuable resource for mathematicians and mathematical physicists wanting to learn renormalisation group theory.

Probability and Statistical Physics in St. Petersburg

Author : V. Sidoravicius
Publisher : American Mathematical Soc.
ISBN 13 : 1470422484
Total Pages : 482 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Probability and Statistical Physics in St. Petersburg by : V. Sidoravicius

Download or read book Probability and Statistical Physics in St. Petersburg written by V. Sidoravicius and published by American Mathematical Soc.. This book was released on 2016-04-28 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings a reader to the cutting edge of several important directions of the contemporary probability theory, which in many cases are strongly motivated by problems in statistical physics. The authors of these articles are leading experts in the field and the reader will get an exceptional panorama of the field from the point of view of scientists who played, and continue to play, a pivotal role in the development of the new methods and ideas, interlinking it with geometry, complex analysis, conformal field theory, etc., making modern probability one of the most vibrant areas in mathematics.

In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius

Author : Maria Eulália Vares
Publisher : Springer Nature
ISBN 13 : 3030607542
Total Pages : 819 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius by : Maria Eulália Vares

Download or read book In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius written by Maria Eulália Vares and published by Springer Nature. This book was released on 2021-03-25 with total page 819 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Séminaire de Probabilités XLVIII

Author : Catherine Donati-Martin
Publisher : Springer
ISBN 13 : 3319444654
Total Pages : 503 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Séminaire de Probabilités XLVIII by : Catherine Donati-Martin

Download or read book Séminaire de Probabilités XLVIII written by Catherine Donati-Martin and published by Springer. This book was released on 2016-11-17 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: In addition to its further exploration of the subject of peacocks, introduced in recent Séminaires de Probabilités, this volume continues the series’ focus on current research themes in traditional topics such as stochastic calculus, filtrations and random matrices. Also included are some particularly interesting articles involving harmonic measures, random fields and loop soups. The featured contributors are Mathias Beiglböck, Martin Huesmann and Florian Stebegg, Nicolas Juillet, Gilles Pags, Dai Taguchi, Alexis Devulder, Mátyás Barczy and Peter Kern, I. Bailleul, Jürgen Angst and Camille Tardif, Nicolas Privault, Anita Behme, Alexander Lindner and Makoto Maejima, Cédric Lecouvey and Kilian Raschel, Christophe Profeta and Thomas Simon, O. Khorunzhiy and Songzi Li, Franck Maunoury, Stéphane Laurent, Anna Aksamit and Libo Li, David Applebaum, and Wendelin Werner.