## Random Walks and Geometry: Proceedings of a Workshop at the Erwin Schrödinger Institute, Vienna, June 18-July 13, 2001Recent developments show that probability methods have become a very powerful tool in such different areas as statistical physics, dynamical systems, Riemannian geometry, group theory, harmonic analysis, graph theory and computer science. This volume is an outcome of the special semester 2001 - Random Walks held at the Schrödinger Institute in Vienna, Austria. It contains original research articles with non-trivial new approaches based on applications of random walks and similar processes to Lie groups, geometric flows, physical models on infinite graphs, random number generators, Lyapunov exponents, geometric group theory, spectral theory of graphs and potential theory. Highlights are the first survey of the theory of the stochastic Loewner evolution and its applications to percolation theory (a new rapidly developing and very promising subject at the crossroads of probability, statistical physics and harmonic analysis), surveys on expander graphs, random matrices and quantum chaos, cellular automata and symbolic dynamical systems, and others. The contributors to the volume are the leading experts in the area. The book will provide a valuable source both for active researchers and graduate students in the respective fields. |

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### Contents

Raffaella Burioni Davide Cassi and Alessandro Vezzani | 36 |

Random walks | 42 |

Harmonic oscillations | 55 |

Introduction | 61 |

Tullio CeccheriniSilberstein Francesca Fiorenzi and Fabio Scarabotti | 73 |

Alex Gamburd | 109 |

Grigorchuk and Andrzej Zuk | 141 |

Yves Guivarch et Émile Le Page | 181 |

Enrique Bendito Ángeles Carmona and Andrés M Encinas | 363 |

Sébastien Blachère | 377 |

Massimo Campanino and Dimitri Petritis | 393 |

Tullio CeccheriniSilberstein and Fabio Scarabotti | 413 |

Alex Eskin and Gregory Margulis | 431 |

Alessandra Iozzi | 445 |

Anders Karlsson | 459 |

Anna Maria Mantero and Anna Zappa | 473 |

Gregory F Lawler | 261 |

George A Willis | 295 |

Martine Babillot | 319 |

Martin T Barlow and Steven N Evans | 337 |

Laurent Bartholdi | 349 |

Tatiana Nagnibeda | 487 |

Sam Northshield | 501 |

Laurent SaloffCoste | 515 |

### Other editions - View all

Random Walks and Geometry: Proceedings of a Workshop at the Erwin ... Vadim Kaimanovich Limited preview - 2004 |