Geoffrey Grimmett

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Books By Geoffrey Grimmett

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Probability on Graphs: Random Processes on Graphs and Lattices (Institute of Mathematical Statistics Textbooks Book 8) 25-Jan-2018

by Geoffrey Grimmett

( 8 )

$25.34 $46.77

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.

Other Formats:: Hardcover , Paperback

The Random-Cluster Model (Grundlehren der mathematischen Wissenschaften Book 333) 13-Dec-2006

by Geoffrey R. Grimmett

$128.44 $145.70

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.

Other Formats:: Hardcover , Paperback

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Geoffrey Grimmett

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