## Stochastic Processes, Physics and Geometry: New Interplays. I: New Interplays : a Volume in Honor of Sergio Albeverio : Proceedings of the Conference on Infinite Dimensional (Stochastic) Analysis and Quantum Physics, Max Planck Institute for Mathematics in the Sciences, Leipzig, January 18-22, 1999This volume and Stochastic Processes, Physics and Geometry: New Interplays. II present state-of-the-art research currently unfolding at the interface between mathematics and physics. Included are select articles from the international conference held in Leipzig (Germany) in honor of Sergio Albeverio's sixtieth birthday. The theme of the conference, ``Infinite Dimensional (Stochastic) Analysis and Quantum Physics'', was chosen to reflect Albeverio's wide-ranging scientific interests. The articles in these books reflect that broad range of interests and provide a detailed overview highlighting the deep interplay among stochastic processes, mathematical physics, and geometry. The contributions are written by internationally recognized experts in the fields of stochastic analysis, linear and nonlinear (deterministic and stochastic) PDEs, infinite dimensional analysis, functional analysis, commutative and noncommutative probability theory, integrable systems, quantum and statistical mechanics, geometric quantization, and neural networks. Also included are applications in biology and other areas. Most of the contributions are high-level research papers. However, there are also some overviews on topics of general interest. The articles selected for publication in these volumes were specifically chosen to introduce readers to advanced topics, to emphasize interdisciplinary connections, and to stress future research directions. Volume I contains contributions from invited speakers; Volume II contains additional contributed papers. |

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### Contents

A Brief Curriculum Vitae of Sergio Albeverio | 1 |

Students and postdoctoral fellows supervised by Sergio Albeverio1 | 3 |

Publications of Sergio Albeverio1 | 9 |

On the occasion of Sergio Albeverios 60th birthday | 37 |

Growth and saturation in random media | 41 |

Maximal Inequalities and Exponential Estimates for Stochastic Convolutions in Banach Spaces | 55 |

On Markov evolution equations in quotient probability spaces | 65 |

Maximal dissipativity of the Dirichlet operator corresponding to the Burgers equation | 85 |

Special Ito maps and an L2 Hodge theory for one forms on path spaces | 145 |

The classical massive Thirring system revisited | 163 |

On Itos formulae for additive functionals of symmetric diffusion processes | 201 |

Spectral Theory of Sparse Potentials | 213 |

Invariant measures under Schrodinger evolution and quantum statistical mechanics | 239 |

Exponential mixing for classical continuous systems | 243 |

Diffusions on simple configuration spaces | 255 |

One and twoparticle branches of the spectrum of many component operators | 271 |

in Three Dimensions | 99 |

The Square of Self Intersection Local Time of Brownian Motion | 115 |

On the role of flux in scattering theory | 123 |

3 When do wave functions move freely to infinity? | 128 |

Probability and nonlinear analysis E B Dynkin | 139 |

Representation integrate de fonctionnelles analytiques positives | 283 |

neural networks | 291 |

Path properties of a class of Gaussian processes with applications to spdes | 303 |

Hypercontractivity in NonCommutative Lp Spaces | 323 |

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Stochastic Processes, Physics and Geometry: New Interplays. II: New ... Sergio Albeverio Limited preview - 2000 |

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