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Random Walks on Infinite Graphs and Groups
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  • Cited by 157
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    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.

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    Random Walks on Infinite Graphs and Groups
    • Online ISBN: 9780511470967
    • Book DOI: https://doi.org/10.1017/CBO9780511470967
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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.

Reviews

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

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