Probability on graphs : random processes on graphs and lattices [EBook] / Geoffrey Grimmett, Statistical Laboratory, University of Cambridge.
Probability on graphs : random processes on graphs and lattices [EBook] / Geoffrey Grimmett, Statistical Laboratory, University of Cambridge.
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, selfavoiding walk, interacting particle systems,...
Personal Name(s):  Grimmett, Geoffrey, (author) 

Edition: 
Second edition. 
Imprint: 
Cambridge :
Cambridge University Press,
2018

Physical Description: 
1 online resource (xi, 265 pages) 
Note: 
englisch 
ISBN: 
9781108528986 9781108438179 
Series Title: 
Institute of Mathematical Statistics textbooks ;
8 
Subject (LOC):  
Full Text 
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, selfavoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and randomcluster 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 randomcluster 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. 