The Random Cluster Model On Finite Graphs PDF Download
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Author | : Geoffrey R. Grimmett |
Publisher | : Springer Science & Business Media |
Total Pages | : 392 |
Release | : 2006-12-13 |
Genre | : Mathematics |
ISBN | : 3540328912 |
Download The Random-Cluster Model Book in PDF, ePub and Kindle
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.
Author | : Darion Mayes |
Publisher | : |
Total Pages | : 0 |
Release | : 2022 |
Genre | : |
ISBN | : |
Download The Random Cluster Model on Finite Graphs Book in PDF, ePub and Kindle
Author | : Geoffrey Grimmett |
Publisher | : Cambridge University Press |
Total Pages | : 279 |
Release | : 2018-01-25 |
Genre | : Mathematics |
ISBN | : 1108542999 |
Download Probability on Graphs Book in PDF, ePub and Kindle
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.
Author | : Geoffrey R. Grimmett |
Publisher | : Springer |
Total Pages | : 378 |
Release | : 2009-09-02 |
Genre | : Mathematics |
ISBN | : 9783540821588 |
Download The Random-Cluster Model Book in PDF, ePub and Kindle
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.
Author | : Béla Bollobás |
Publisher | : |
Total Pages | : 32 |
Release | : 1994 |
Genre | : |
ISBN | : |
Download The Random-cluster Model on the Complete Graph Book in PDF, ePub and Kindle
Author | : Rick Durrett |
Publisher | : Cambridge University Press |
Total Pages | : 203 |
Release | : 2010-05-31 |
Genre | : Mathematics |
ISBN | : 1139460889 |
Download Random Graph Dynamics Book in PDF, ePub and Kindle
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.
Author | : |
Publisher | : |
Total Pages | : 18 |
Release | : 1998 |
Genre | : |
ISBN | : |
Download The Random Cluster Model on a General Graph and a Phase Transition Characterization of Nonamendability Book in PDF, ePub and Kindle
Author | : Johan Jonasson |
Publisher | : |
Total Pages | : 18 |
Release | : 1998 |
Genre | : |
ISBN | : |
Download The Random Cluster Model on an General Graph and a Phase Transition Characterization of Nonamenability Book in PDF, ePub and Kindle
Author | : Martin T. Barlow |
Publisher | : Springer Nature |
Total Pages | : 421 |
Release | : 2019-12-03 |
Genre | : Mathematics |
ISBN | : 3030320111 |
Download Random Graphs, Phase Transitions, and the Gaussian Free Field Book in PDF, ePub and Kindle
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 | : Vladas Sidoravicius |
Publisher | : Springer Nature |
Total Pages | : 261 |
Release | : 2019-10-17 |
Genre | : Mathematics |
ISBN | : 9811502986 |
Download Sojourns in Probability Theory and Statistical Physics - II Book in PDF, ePub and Kindle
Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for nearly half a century. This three-volume set is a celebration of the far-reaching scientific impact of his work. It consists of articles by Chuck’s collaborators and colleagues across a number of the fields to which he has made contributions of fundamental significance. This publication was conceived during a conference in 2016 at NYU Shanghai that coincided with Chuck's 70th birthday. The sub-titles of the three volumes are: I. Spin Glasses and Statistical Mechanics II. Brownian Web and Percolation III. Interacting Particle Systems and Random Walks The articles in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate students and researchers who seek initiation and inspiration in Probability Theory and Statistical Physics.