Random Graphs Phase Transitions And The Gaussian Free Field
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Random Graphs Phase Transitions And The Gaussian Free Field
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Author : Martin T. Barlow
language : en
Publisher: Springer Nature
Release Date : 2019-12-03
Random Graphs Phase Transitions And The Gaussian Free Field written by Martin T. Barlow and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-03 with Mathematics categories.
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.
Phase Transitions
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Author : Moshe Gitterman
language : en
Publisher: World Scientific Publishing Company
Release Date : 2013-09-25
Phase Transitions written by Moshe Gitterman and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-25 with Science categories.
This book provides a comprehensive review of the theory of phase transitions and its modern applications, based on the five pillars of the modern theory of phase transitions: the Ising model, mean field, scaling, renormalization group and universality. This expanded second edition includes, along with a description of vortices and high temperature superconductivity, a discussion of phase transitions in chemical reactions and moving systems. The book covers the close connection between phase transitions and small world phenomena as well as scale-free systems such as the stock market and the Internet.
An Introduction To Random Interlacements
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Author : Alexander Drewitz
language : en
Publisher: Springer
Release Date : 2014-05-06
An Introduction To Random Interlacements written by Alexander Drewitz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-06 with Mathematics categories.
This book gives a self-contained introduction to the theory of random interlacements. The intended reader of the book is a graduate student with a background in probability theory who wants to learn about the fundamental results and methods of this rapidly emerging field of research. The model was introduced by Sznitman in 2007 in order to describe the local picture left by the trace of a random walk on a large discrete torus when it runs up to times proportional to the volume of the torus. Random interlacements is a new percolation model on the d-dimensional lattice. The main results covered by the book include the full proof of the local convergence of random walk trace on the torus to random interlacements and the full proof of the percolation phase transition of the vacant set of random interlacements in all dimensions. The reader will become familiar with the techniques relevant to working with the underlying Poisson Process and the method of multi-scale renormalization, which helps in overcoming the challenges posed by the long-range correlations present in the model. The aim is to engage the reader in the world of random interlacements by means of detailed explanations, exercises and heuristics. Each chapter ends with short survey of related results with up-to date pointers to the literature.
Random Graphs
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Author : Svante Janson
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-30
Random Graphs written by Svante Janson and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-30 with Mathematics categories.
A unified, modern treatment of the theory of random graphs-including recent results and techniques Since its inception in the 1960s, the theory of random graphs has evolved into a dynamic branch of discrete mathematics. Yet despite the lively activity and important applications, the last comprehensive volume on the subject is Bollobas's well-known 1985 book. Poised to stimulate research for years to come, this new work covers developments of the last decade, providing a much-needed, modern overview of this fast-growing area of combinatorics. Written by three highly respected members of the discrete mathematics community, the book incorporates many disparate results from across the literature, including results obtained by the authors and some completely new results. Current tools and techniques are also thoroughly emphasized. Clear, easily accessible presentations make Random Graphs an ideal introduction for newcomers to the field and an excellent reference for scientists interested in discrete mathematics and theoretical computer science. Special features include: * A focus on the fundamental theory as well as basic models of random graphs * A detailed description of the phase transition phenomenon * Easy-to-apply exponential inequalities for large deviation bounds * An extensive study of the problem of containing small subgraphs * Results by Bollobas and others on the chromatic number of random graphs * The result by Robinson and Wormald on the existence of Hamilton cycles in random regular graphs * A gentle introduction to the zero-one laws * Ample exercises, figures, and bibliographic references
Graphs Morphisms And Statistical Physics
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Author : Jaroslav Nešetřil
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Graphs Morphisms And Statistical Physics written by Jaroslav Nešetřil and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Science categories.
Based on a March 2001 workshop, this collection explores connections between random graphs and percolation, between slow mixing and phase transition, and between graph morphisms and hard-constraint models. Topics of the 14 papers include efficient local search near phase transitions in combinatorial optimization, graph homomorphisms and long range action, recent results on parameterized H-colorings, the satisfiability of random k-Horn formulae, a discrete non-Pfaffian approach to the Ising problem, and chromatic numbers of products of tournaments. No indexes are provided. Annotation : 2004 Book News, Inc., Portland, OR (booknews.com).
Large Deviations For Random Graphs
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Author : Sourav Chatterjee
language : en
Publisher: Springer
Release Date : 2017-08-31
Large Deviations For Random Graphs written by Sourav Chatterjee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-31 with Mathematics categories.
This book addresses the emerging body of literature on the study of rare events in random graphs and networks. For example, what does a random graph look like if by chance it has far more triangles than expected? Until recently, probability theory offered no tools to help answer such questions. Important advances have been made in the last few years, employing tools from the newly developed theory of graph limits. This work represents the first book-length treatment of this area, while also exploring the related area of exponential random graphs. All required results from analysis, combinatorics, graph theory and classical large deviations theory are developed from scratch, making the text self-contained and doing away with the need to look up external references. Further, the book is written in a format and style that are accessible for beginning graduate students in mathematics and statistics.
Analyticity Results In Bernoulli Percolation
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Author : Agelos Georgakopoulos
language : en
Publisher: American Mathematical Society
Release Date : 2023-09-15
Analyticity Results In Bernoulli Percolation written by Agelos Georgakopoulos and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-15 with Mathematics categories.
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Fundamental Factorization Of A Glsm Part I Construction
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Author : Ionut Ciocan-Fontanine
language : en
Publisher: American Mathematical Society
Release Date : 2023-09-27
Fundamental Factorization Of A Glsm Part I Construction written by Ionut Ciocan-Fontanine and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-27 with Mathematics categories.
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Random Graph Dynamics
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Author : Rick Durrett
language : en
Publisher: Cambridge University Press
Release Date : 2010-05-31
Random Graph Dynamics written by Rick Durrett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-31 with Mathematics categories.
The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.
Methods Of Contemporary Mathematical Statistical Physics
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Author : Marek Biskup
language : en
Publisher: Springer
Release Date : 2009-07-31
Methods Of Contemporary Mathematical Statistical Physics written by Marek Biskup and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-31 with Mathematics categories.
This volume presents a collection of courses introducing the reader to the recent progress with attention being paid to laying solid grounds and developing various basic tools. It presents new results on phase transitions for gradient lattice models.