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Author: Geoffrey R. Grimmett
Publisher: Springer Science & Business Media
ISBN: 3540328912
Category : Mathematics
Languages : en
Pages : 392
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Book Description
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: Geoffrey R. Grimmett
Publisher: Springer Science & Business Media
ISBN: 3540328912
Category : Mathematics
Languages : en
Pages : 392
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Book Description
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:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author: Geoffrey Grimmett
Publisher: Cambridge University Press
ISBN: 1108542999
Category : Mathematics
Languages : en
Pages : 279
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Book Description
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
ISBN: 9783540821588
Category : Mathematics
Languages : en
Pages : 378
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Book Description
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:
ISBN:
Category :
Languages : en
Pages : 32
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Book Description
Author: Rick Durrett
Publisher: Cambridge University Press
ISBN: 1139460889
Category : Mathematics
Languages : en
Pages : 203
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Book Description
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:
ISBN:
Category :
Languages : en
Pages : 18
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Book Description
Author: Johan Jonasson
Publisher:
ISBN:
Category :
Languages : en
Pages : 18
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Book Description
Author: Martin T. Barlow
Publisher: Springer Nature
ISBN: 3030320111
Category : Mathematics
Languages : en
Pages : 421
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Book Description
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: Remco van der Hofstad
Publisher: Cambridge University Press
ISBN: 110717287X
Category : Computers
Languages : en
Pages : 341
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Book Description
This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.
