Random Walks, Boundaries and Spectra [electronic resource] /
Lenz, Daniel.editor.
Sobieczky, Florian.editor.
Woess, Wolfgang.editor.
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'. Contributors: M. Arnaudon A. Bendikov M. Björklund B. Bobikau D. D'Angeli A. Donno M.J. Dunwoody A. Erschler R. Froese A. Gnedin Y. Guivarc'h S. Haeseler D. Hasler P.E.T. Jorgensen M. Keller I. Krasovsky P. Müller T. Nagnibeda J. Parkinson E.P.J. Pearse C. Pittet C.R.E. Raja B. Schapira W. Spitzer P. Stollmann A. Thalmaier T.S. Turova R.K. Wojciechowski.
Description based upon print version of record.
On Continuity of Range, Entropy and Drift for Random Walks on Groups1. Introduction; 2. Range and entropy; 2.1. Continuity of range for symmetric measures; 2.2. Discontinuity of range and entropy; 3. Random walks on Z  A; 4. Symmetric examples of discontinuity of drift; References; Polynomial Growth, Recurrence and Ergodicityfor Random Walks on Locally Compact Groups and Homogeneous Spaces; 1. Introduction; 2. Polynomial growth; 3. Transience and recurrence; 3.1. Definitions; 3.2. Examples; 4. Growth and recurrence; 5. Linear groups over local fields; 6. Homogeneous spaces; 6.1. A framework
6.2. An example6.3. A question; References; Ergodic Theorems for Homogeneous Dilations; 1. Introduction; 2. Measure theory and Fourier analysis; 2.1. Basic measure theory; 2.2. Fourier analysis; 3. Ergodic theorems; 3.1. Mean ergodic theorems; 3.2. Pointwise ergodic theorems; 3.3. Maximal inequalities; 3.4. Rubio de Francia's maximal inequality; 4. Applications; 4.1. Ergodic theorems for dilations of submanifolds; 4.2. Ergodic theorems for polynomial curves; 4.3. Ergodic theorems for Salem sets; 4.4. Regularity of return times; References; Boundaries from Inhomogeneous Bernoulli Trials
1. Introduction2. Weighted Pascal graphs; 3. Probability of the first head; 4. Transformations of weights; 5. Generalized Stirling triangles; 5.1. The linear weights; 5.2. Generalized Stirling-I; 5.2.1. The case of continuous boundary.; 5.2.2. The case of discrete boundary.; 5.3. Generalized Stirling-II; 6. Generalized Eulerian triangles; Acknowledgment; References; Resistance Boundaries of Infinite Networks; 1. Introduction; 2. The energy space HE; 2.1. The finitely-supported functions and the harmonic functions; 2.2. Monopoles; 3. The discrete Gauss-Green formula; 3.1. Relating Δ to E
3.2. More about monopoles and the spaceM
Includes bibliographical references.
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'. Contributors: M. Arnaudon A. Bendikov M. Björklund B. Bobikau D. D'Angeli A. Donno M.J. Dunwoody A. Erschler R. Froese A. Gnedin Y. Guivarc'h S. Haeseler D. Hasler P.E.T. Jorgensen M. Keller I. Krasovsky P. Müller T. Nagnibeda J. Parkinson E.P.J. Pearse C. Pittet C.R.E. Raja B. Schapira W. Spitzer P. Stollmann A. Thalmaier T.S. Turova R.K. Wojciechowski.
Probabilities.
Probability Theory and Stochastic Processes.