Lecture Notes on the Gaussian Free Field
Author | : Wendelin Werner |
Publisher | : |
Total Pages | : |
Release | : 2021 |
Genre | : |
ISBN | : 9782856299524 |
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Author | : Wendelin Werner |
Publisher | : |
Total Pages | : |
Release | : 2021 |
Genre | : |
ISBN | : 9782856299524 |
Author | : Martin T. Barlow |
Publisher | : Springer Nature |
Total Pages | : 421 |
Release | : 2019-12-03 |
Genre | : Mathematics |
ISBN | : 3030320111 |
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.
Author | : Scott Sheffield |
Publisher | : |
Total Pages | : 194 |
Release | : 2005 |
Genre | : Gibbs' free energy |
ISBN | : |
Author | : Alain-Sol Sznitman |
Publisher | : European Mathematical Society |
Total Pages | : 128 |
Release | : 2012 |
Genre | : Gaussian processes |
ISBN | : 9783037191095 |
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.
Author | : Nam-Gyu Kang |
Publisher | : |
Total Pages | : 0 |
Release | : 2013 |
Genre | : Algebraic fields |
ISBN | : 9782856293690 |
In these mostly expository lectures, the authors give an elementary introduction to conformal field theory in the context of probability theory and complex analysis. The authors consider statistical fields and define Ward functionals in terms of their Lie derivatives. Based on this approach, the authors explain some equations of conformal field theory and outline their relation to SLE theory.
Author | : Anton Bovier |
Publisher | : Springer |
Total Pages | : 254 |
Release | : 2015-09-21 |
Genre | : Science |
ISBN | : 3319193392 |
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.
Author | : Vadim Gorin |
Publisher | : Cambridge University Press |
Total Pages | : 261 |
Release | : 2021-09-09 |
Genre | : Language Arts & Disciplines |
ISBN | : 1108843964 |
This is the first book dedicated to reviewing the mathematics of random tilings of large domains on the plane.
Author | : Sacha Friedli |
Publisher | : Cambridge University Press |
Total Pages | : 643 |
Release | : 2017-11-23 |
Genre | : Mathematics |
ISBN | : 1107184827 |
A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Author | : Daniel S. Freed |
Publisher | : American Mathematical Soc. |
Total Pages | : 476 |
Release | : 1995 |
Genre | : Science |
ISBN | : 9780821886830 |
The first title in a new series, this book explores topics from classical and quantum mechanics and field theory. The material is presented at a level between that of a textbook and research papers making it ideal for graduate students. The book provides an entree into a field that promises to remain exciting and important for years to come.
Author | : Catherine Donati-Martin |
Publisher | : Springer |
Total Pages | : 503 |
Release | : 2016-11-17 |
Genre | : Mathematics |
ISBN | : 3319444654 |
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.