Probability on Graphs: Random Processes on Graphs and Lattices

Author:   Geoffrey Grimmett (University of Cambridge)
Publisher:   Cambridge University Press
Volume:   1
ISBN:  

9780511762550


Publication Date:   05 June 2012
Format:   Undefined
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Probability on Graphs: Random Processes on Graphs and Lattices


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Author:   Geoffrey Grimmett (University of Cambridge)
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press (Virtual Publishing)
Volume:   1
ISBN:  

9780511762550


ISBN 10:   0511762550
Publication Date:   05 June 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Undefined
Publisher's Status:   Active
Availability:   Available To Order   Availability explained
We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately.

Table of Contents

Preface; 1. Random walks on graphs; 2. Uniform spanning tree; 3. Percolation and self-avoiding walk; 4. Association and influence; 5. Further percolation; 6. Contact process; 7. Gibbs states; 8. Random-cluster model; 9. Quantum Ising model; 10. Interacting particle systems; 11. Random graphs; 12. Lorentz gas; References; Index.

Reviews

The book under review serves admirably for this getting started purpose. It provides a rigorous introduction to a broad range of topics centered on the percolation-IPS field discussed above... This book, like a typical Part III course, requires only undergraduate background knowledge but assumes a higher level of general mathematical sophistication. It also requires active engagement by the reader. As I often tell students, Mathematics is not a spectator sport - you learn by actually doing the exercises! For the reader who is willing to engage the material and is not fazed by the fact that some proofs are only outlined or are omitted, this style enables the author to cover a lot of ground in 247 pages. David Aldous, Bulletin of the American Mathematical Society It is written in a condensed style with only the briefest of introductions or motivations, but it is a mine of information for those who are well prepared and know how to use it. It formed the basis for a Probability reading group at the University of Warwick last term and was well received, and parts of it are being used by a colleague for an undergraduate module this term on Probability and Discrete Mathematics. R.S. MacKay, Contemporary Physics


'The book under review serves admirably for this 'getting started' purpose. It provides a rigorous introduction to a broad range of topics centered on the percolation-IPS field discussed above ... This book, like a typical Part III course, requires only undergraduate background knowledge but assumes a higher level of general mathematical sophistication. It also requires active engagement by the reader. As I often tell students, 'Mathematics is not a spectator sport - you learn by actually doing the exercises!' For the reader who is willing to engage the material and is not fazed by the fact that some proofs are only outlined or are omitted, this style enables the author to cover a lot of ground in 247 pages.' David Aldous, Bulletin of the American Mathematical Society 'It is written in a condensed style with only the briefest of introductions or motivations, but it is a mine of information for those who are well prepared and know how to use it. It formed the basis for a Probability reading group at the University of Warwick last term and was well received, and parts of it are being used by a colleague for an undergraduate module this term on Probability and Discrete Mathematics.' R.S. MacKay, Contemporary Physics 'This is clearly a successful advanced textbook.' Fernando Q. Gouvea, MAA Reviews The book under review serves admirably for this getting started purpose. It provides a rigorous introduction to a broad range of topics centered on the percolation-IPS field discussed above... This book, like a typical Part III course, requires only undergraduate background knowledge but assumes a higher level of general mathematical sophistication. It also requires active engagement by the reader. As I often tell students, Mathematics is not a spectator sport - you learn by actually doing the exercises! For the reader who is willing to engage the material and is not fazed by the fact that some proofs are only outlined or are omitted, this style enables the author to cover a lot of ground in 247 pages. David Aldous, Bulletin of the American Mathematical Society It is written in a condensed style with only the briefest of introductions or motivations, but it is a mine of information for those who are well prepared and know how to use it. It formed the basis for a Probability reading group at the University of Warwick last term and was well received, and parts of it are being used by a colleague for an undergraduate module this term on Probability and Discrete Mathematics. R.S. MacKay, Contemporary Physics 'This is clearly a successful advanced textbook.' Fernando Q. Gouvea, MAA Reviews


Author Information

Geoffrey Grimmett is Professor of Mathematical Statistics in the Statistical Laboratory at the University of Cambridge.

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