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Random Walks, Boundaries and Spectra

Part of the Progress in Probability Book Series (volume 64)

Editors: Lenz, Daniel; Sobieczky, Florian; Woess, Wolfgang

DOI: 10.1007/978-3-0346-0244-0

ISBN: 978-3-0346-0243-3

Publisher: Springer Basel - Springer Journals

Apr 19, 2011

1 - 10 of 16 Chapters

LitStream

Chapter 1An Inaccessible Graph

Dunwoody, M. J.

Pages: 1 –14

[An inaccessible, vertex transitive, locally finite graph is described. This graph is not quasi-isometric to a Cayley graph.]
LitStream

Chapter 2A Local Limit Theorem for Random Walks on the Chambers of Ã2 Buildings

Parkinson, James; Schapira, Bruno

Pages: 15 –53

[In this paper we outline an approach for analysing random walks on the chambers of buildings. The types of walks that we consider are those which are well adapted to the structure of the building: Namely walks with transition probabilities p(c, d) depending only on the Weyl distance d(c, d). We...
LitStream

Chapter 3On Continuity of Range, Entropy and Drift for Random Walks on Groups

Erschler, Anna

Pages: 55 –64

[We study continuity of various characteristics of random walks on groups with respect to strong convergence of measures.]
LitStream

Chapter 4Polynomial Growth, Recurrence and Ergodicity for Random Walks on Locally Compact Groups and Homogeneous Spaces

Guivarc’h, Yves; Raja, C. R. E.

Pages: 65 –74

[Let G be a locally compact group, E a homogeneous space of G. We discuss the relations between recurrence of a random walk on G or E, ergodicity of the corresponding transformations and polynomial growth of G or E. We consider the special case of linear groups over local fields.]
LitStream

Chapter 5Ergodic Theorems for Homogeneous Dilations

Björklund, Michael

Pages: 75 –89

[In this paper we prove a general ergodic theorem for ergodic and measure-preserving actions of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
LitStream

Chapter 6Boundaries from Inhomogeneous Bernoulli Trials

Gnedin, Alexander

Pages: 91 –110

[The boundary problem is considered for inhomogeneous increasing random walks on the square lattice \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
LitStream

Chapter 7Resistance Boundaries of Infinite Networks

Jorgensen, Palle E. T.; Pearse, Erin P. J.

Pages: 111 –142

[A resistance network is a connected graph (G, c). The conductance function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
LitStream

Chapter 8Brownian Motion and Negative Curvature

Arnaudon, Marc; Thalmaier, Anton

Pages: 143 –161

[It is well known that on a Riemannian manifold, there is a deep interplay between geometry, harmonic function theory, and the long-term behaviour of Brownian motion. Negative curvature amplifies the tendency of Brownian motion to exit compact sets and, if topologically possible, to wander out to...
LitStream

Chapter 9Stochastically Incomplete Manifolds and Graphs

Wojciechowski, Radosław Krzysztof

Pages: 163 –179

[We survey geometric properties which imply the stochastic incompleteness of the minimal diffusion process associated to the Laplacian on manifolds and graphs. In particular, we completely characterize stochastic incompleteness for spherically symmetric graphs and show that, in contrast to the...
LitStream

Chapter 10Generalized Solutions and Spectrum for Dirichlet Forms on Graphs

Haeseler, Sebastian; Keller, Matthias

Pages: 181 –199

[In the framework of regular Dirichlet forms we consider operators on infinite graphs. We study the connection of the existence of solutions with certain properties and the spectrum of the operators. In particular we prove a version of the Allegretto-Piepenbrink theorem which says that positive...

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