Skip to main content Accessibility help
Random Walks on Infinite Graphs and Groups
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 157
  • Cited by
    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Kostenko, Aleksey and Nicolussi, Noema 2019. Spectral estimates for infinite quantum graphs. Calculus of Variations and Partial Differential Equations, Vol. 58, Issue. 1,

    Keller, Matthias Pinchover, Yehuda and Pogorzelski, Felix 2018. Optimal Hardy inequalities for Schrödinger operators on graphs. Communications in Mathematical Physics, Vol. 358, Issue. 2, p. 767.

    Vershik, Anatoly M. and Malyutin, Andrei V. 2018. The absolute of finitely generated groups: I. Commutative (semi)groups. European Journal of Mathematics, Vol. 4, Issue. 4, p. 1476.

    Vershik, A. M. and Malyutin, A. V. 2018. The Absolute of Finitely Generated Groups: II. The Laplacian and Degenerate Parts. Functional Analysis and Its Applications, Vol. 52, Issue. 3, p. 163.

    Bartholdi, Laurent 2018. Sequences, Groups, and Number Theory. p. 433.

    JUSCHENKO, KATE MATTE BON, NICOLÁS MONOD, NICOLAS and DE LA SALLE, MIKAEL 2018. Extensive amenability and an application to interval exchanges. Ergodic Theory and Dynamical Systems, Vol. 38, Issue. 01, p. 195.

    Deuschel, Jean-Dominique Nguyen, Tuan Anh and Slowik, Martin 2018. Quenched invariance principles for the random conductance model on a random graph with degenerate ergodic weights. Probability Theory and Related Fields, Vol. 170, Issue. 1-2, p. 363.

    Luo, Jun Jason 2018. On the Lipschitz equivalence of self-affine sets. Mathematische Nachrichten,

    Foley, R. D. and McDonald, D. R. 2018. Yaglom limits can depend on the starting state. Advances in Applied Probability, Vol. 50, Issue. 01, p. 1.

    Bezuglyi, Sergey and Jorgensen, Palle E. T. 2018. Monopoles, Dipoles, and Harmonic Functions on Bratteli Diagrams. Acta Applicandae Mathematicae,

    Exner, Pavel Kostenko, Aleksey Malamud, Mark and Neidhardt, Hagen 2018. Spectral Theory of Infinite Quantum Graphs. Annales Henri Poincaré, Vol. 19, Issue. 11, p. 3457.

    Hutchcroft, Tom and Peres, Yuval 2018. The component graph of the uniform spanning forest: transitions in dimensions $$9,10,11,\ldots $$9,10,11,…. Probability Theory and Related Fields,

    Gray, Robert D and Kambites, Mark 2018. On Cogrowth, Amenability, and the Spectral Radius of a Random Walk on a Semigroup. International Mathematics Research Notices,

    Вершик, Анатолий Моисеевич Vershik, Anatolii Moiseevich Малютин, Андрей Валерьевич and Malyutin, Andrei Valer'evich 2018. Абсолют конечно порожденных групп: II. Лапласова и вырожденная части. Функциональный анализ и его приложения, Vol. 52, Issue. 3, p. 3.

    Luo, Jun Jason 2018. Self-similar sets, simple augmented trees and their Lipschitz equivalence. Journal of the London Mathematical Society,

    Bücking, Ulrike 2018. On Rigidity and Convergence of Circle Patterns. Discrete & Computational Geometry,

    Gouëzel, Sébastien Mathéus, Frédéric and Maucourant, François 2018. Entropy and drift in word hyperbolic groups. Inventiones mathematicae, Vol. 211, Issue. 3, p. 1201.

    HAMANN, MATTHIAS 2018. On the tree-likeness of hyperbolic spaces. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 164, Issue. 02, p. 345.

    Forghani, Behrang and Mallahi-Karai, Keivan 2018. Positive Harmonic Functions of Transformed Random Walks. Potential Analysis,

    Kumagai, Takashi and Nakamura, Chikara 2018. Lamplighter Random Walks on Fractals. Journal of Theoretical Probability, Vol. 31, Issue. 1, p. 68.

  • Export citation
  • Recommend to librarian
  • Recommend this book

    Email your librarian or administrator to recommend adding this book to your organisation's collection.

    Random Walks on Infinite Graphs and Groups
    • Online ISBN: 9780511470967
    • Book DOI:
    Please enter your name
    Please enter a valid email address
    Who would you like to send this to *
  • Buy the print book

Book description

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.


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 Source: Bulletin of the London Mathematical Society

Review of the hardback:‘… will be essential reading for all researchers in stochastic processes and related topics.’

Source: European Maths Society Journal

Refine List
Actions for selected content:
Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Send to Kindle
  • Send to Dropbox
  • Send to Google Drive
  • Send content to

    To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to .

    To send content items to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

    Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

    Find out more about the Kindle Personal Document Service.

    Please be advised that item(s) you selected are not available.
    You are about to send

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.


Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed