Random Walks, Boundaries and Spectra

1. Front Matter

   Pages i-xxvi

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2. An Inaccessible Graph

   • M. J. Dunwoody

   Pages 1-14

3. A Local Limit Theorem for Random Walks on the Chambers of Ã2 Buildings

   • James Parkinson, Bruno Schapira

   Pages 15-53

4. On Continuity of Range, Entropy and Drift for Random Walks on Groups

   • Anna Erschler

   Pages 55-64

5. Polynomial Growth, Recurrence and Ergodicity for Random Walks on Locally Compact Groups and Homogeneous Spaces

   • Yves Guivarc’h, C. R. E. Raja

   Pages 65-74

6. Ergodic Theorems for Homogeneous Dilations

   • Michael Björklund

   Pages 75-89

7. Boundaries from Inhomogeneous Bernoulli Trials

   • Alexander Gnedin

   Pages 91-110

8. Resistance Boundaries of Infinite Networks

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

   Pages 111-142

9. Brownian Motion and Negative Curvature

   • Marc Arnaudon, Anton Thalmaier

   Pages 143-161

10. Stochastically Incomplete Manifolds and Graphs

    • Radosław Krzysztof Wojciechowski

    Pages 163-179

11. Generalized Solutions and Spectrum for Dirichlet Forms on Graphs

    • Sebastian Haeseler, Matthias Keller

    Pages 181-199

12. A Geometric Approach to Absolutely Continuous Spectrum for Discrete Schrödinger Operators

    • Richard Froese, David Hasler, Wolfgang Spitzer

    Pages 201-226

13. Some Spectral and Geometric Aspects of Countable Groups

    • Alexander Bendikov, Barbara Bobikau, Christophe Pittet

    Pages 227-234

14. Percolation Hamiltonians

    • Peter Müller, Peter Stollmann

    Pages 235-258

15. Survey of Scalings for the Largest Connected Component in Inhomogeneous Random Graphs

    • Tatyana S. Turova

    Pages 259-275

16. Partition Functions of the Ising Model on Some Self-similar Schreier Graphs

    • Daniele D’Angeli, Alfredo Donno, Tatiana Nagnibeda

    Pages 277-304

17. Aspects of Toeplitz Determinants

    • Igor Krasovsky

    Pages 305-324

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, Austria) between June 29th and July 5th, 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'.

• Mathematisches Inst., Universität Jena, Jena, Germany

  Daniel Lenz

• Inst. Mathematik C, TU Graz, Graz, Austria

  Florian Sobieczky, Wolfgang Woess

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