Skip to content
Open global navigation

Cambridge University Press

AcademicLocation selectorSearch toggleMain navigation toggle
Cart
Register Sign in Wishlist

Probability on Graphs
Random Processes on Graphs and Lattices

$39.99

textbook

Part of Institute of Mathematical Statistics Textbooks

  • Date Published: August 2010
  • availability: In stock
  • format: Paperback
  • isbn: 9780521147354

$39.99
Paperback

Add to cart Add to wishlist

Other available formats:
Hardback, eBook


Looking for an examination copy?

If you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact collegesales@cambridge.org providing details of the course you are teaching.

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • 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. Schramm–Löwner evolutions (SLE) arise in various contexts. The choice of topics is strongly motivated by modern applications and focuses on areas that merit further research. Special features include a simple account of Smirnov's proof of Cardy's formula for critical percolation, and a fairly full account of the theory of influence and sharp-thresholds. 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 renowned for his clear, readable style
    • Probability theory sheds light on everything
    • Engages your brain and gets your hands dirty
    Read more

    Reviews & endorsements

    "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

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Date Published: August 2010
    • format: Paperback
    • isbn: 9780521147354
    • length: 257 pages
    • dimensions: 227 x 150 x 15 mm
    • weight: 0.42kg
    • contains: 45 b/w illus. 90 exercises
    • availability: In stock
  • 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.

  • general resources

    View all resources
    Group Section Name Type Size Sort Order filter vars
    General ResourcesAuthor's web pagelinkn/aSort Order general resources general resources general resources general resources

    These resources are provided free of charge by Cambridge University Press with permission of the author of the corresponding work, but are subject to copyright. You are permitted to view, print and download these resources for your own personal use only, provided any copyright lines on the resources are not removed or altered in any way. Any other use, including but not limited to distribution of the resources in modified form, or via electronic or other media, is strictly prohibited unless you have permission from the author of the corresponding work and provided you give appropriate acknowledgement of the source.

    If you are having problems accessing these resources please email cflack@cambridge.org

  • Author

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

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

You are now leaving the Cambridge University Press website, your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Find content that relates to you

© Cambridge University Press 2014

Back to top

Are you sure you want to delete your account?

This cannot be undone.

Cancel Delete

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×