Skip to content
Register Sign in Wishlist

Random Walks on Infinite Graphs and Groups

£54.99

Part of Cambridge Tracts in Mathematics

  • Date Published: May 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521061728

£ 54.99
Paperback

Add to cart Add to wishlist

Other available formats:
Hardback, eBook


Looking for an inspection copy?

This title is not currently available on inspection

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • The main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory. The author considers Markov chains whose state space is equipped with the structure of an infinite, locally finite graph, or as a particular case, of a finitely generated group. The transition probabilities are assumed to be adapted to the underlying structure in some way that must be specified precisely in each case. From the probabilistic viewpoint, the question is what impact the particular type of structure has on various aspects of the behaviour of the random walk. Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. Links with spectral theory and discrete potential theory are also discussed. This book will be essential reading for all researchers working in stochastic process and related topics.

    • Wide-ranging treatment that connects to many other areas of mathematics
    • Author is acknowledged expert in the field
    • Exciting area
    Read more

    Reviews & endorsements

    Review of the hardback: 'This is an excellent book, where beginners and specialists alike will find useful information. It will become one of the major references for all those interested directly or indirectly in random walks. I highly recommend it.' L. Saloff-Coste, Bulletin of the London Mathematical Society

    Review of the hardback: '… will be essential reading for all researchers in stochastic processes and related topics.' European Maths Society Journal

    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: May 2008
    • format: Paperback
    • isbn: 9780521061728
    • length: 352 pages
    • dimensions: 229 x 152 x 20 mm
    • weight: 0.52kg
    • contains: 12 b/w illus.
    • availability: Available
  • Table of Contents

    Part I. The Type Problem:
    1. Basic facts
    2. Recurrence and transience of infinite networks
    3. Applications to random walks
    4. Isoperimetric inequalities
    5. Transient subtrees, and the classification of the recurrent quasi transitive graphs
    6. More on recurrence
    Part II. The Spectral Radius:
    7. Superharmonic functions and r-recurrence
    8. The spectral radius
    9. Computing the Green function
    10. Spectral radius and strong isoperimetric inequality
    11. A lower bound for simple random walk
    12. Spectral radius and amenability
    Part III. The Asymptotic Behaviour of Transition Probabilities:
    13. The local central limit theorem on the grid
    14. Growth, isoperimetric inequalities, and the asymptotic type of random walk
    15. The asymptotic type of random walk on amenable groups
    16. Simple random walk on the Sierpinski graphs
    17. Local limit theorems on free products
    18. Intermezzo
    19. Free groups and homogenous trees
    Part IV. An Introduction to Topological Boundary Theory:
    20. Probabilistic approach to the Dirichlet problem, and a class of compactifications
    21. Ends of graphs and the Dirichlet problem
    22. Hyperbolic groups and graphs
    23. The Dirichlet problem for circle packing graphs
    24. The construction of the Martin boundary
    25. Generalized lattices, Abelian and nilpotent groups, and graphs with polynomial growth
    27. The Martin boundary of hyperbolic graphs
    28. Cartesian products.

  • Author

    Wolfgang Woess, Technische Universität Graz, Austria

Related Books

also by this author

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

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 ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon
×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

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.
×