Random Walks, Boundaries and Spectra

These proceedings represent the current state of research on the topics 'boundary theory' and 'spectral and probability theory' of random walks on infinite graphs. They are the result of the two workshops held in Styria (Graz and St. Kathrein am Offenegg) between the 29th of June, and 5th of July, 2009. Many of the participants joined both meetings. Even though the perspectives range from very different fields of mathematics, they all contribute with important results to the same wonderful topic from structure theory, which, by extending a quotation of Laurent Saloff-Coste, could be described by 'exploration of groups by random processes'.

Preface	p. ix
Programme of the Workshop on "Boundaries"	p. xi
Programme of the Alp-Workshop 2009	p. xiii
Publications of D.I. Cartwright	p. xv
Publications of M.A. Picardello	p. xviii
Publications of V.A. Kaimanovich	p. xxii
An Inaccessible Graph	p. 1
A Local Limit Theorem for Random Walks on the Chambers of A2 Buildings	p. 15
On Continuity of Range, Entropy and Drift for Random Walks on Groups	p. 55
Polynomial Growth, Recurrence and Ergodicity for Random Walks on Locally Compact Groups and Homogeneous Spaces	p. 65
Ergodic Theorems for Homogeneous Dilations	p. 75
Boundaries from Inhomogeneous Bernoulli Trials	p. 91
Resistance Boundaries of Infinite Networks	p. 111
Brownian Motion and Negative Curvature	p. 143
Stochastically Incomplete Manifolds and Graphs	p. 163
Generalized Solutions and Spectrum for Dirichlet Forms on Graphs	p. 181
A Geometric Approach to Absolutely Continuous Spectrum for Discrete Schr?dinger Operators	p. 201
Some Spectral and Geometric Aspects of Countable Groups	p. 227
Percolation Hamiltonians	p. 235
Survey of Scalings for the Largest Connected Component in Inhomogeneous Random Graphs	p. 259
Partition Functions of the Ising Model on Some Self-similar Schreier Graphs	p. 277
Aspects of Toeplitz Determinants	p. 305
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Random Walks, Boundaries and Spectra

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