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Stochastic Processes, Physics and Geometry: New Interplays. I: A Volume in Honor of Sergio Albeverio
Edited by: Fritz Gesztesy, University of Missouri, Columbia, MO, Helge Holden, Norwegian University of Science and Technology, Trondheim, Norway, Jürgen Jost, Max Planck Institut für Mathematik, Leipzig, Germany, Sylvie Paycha, Université Blaise Pascal, Aubiere, France, Michael Röckner, Universität Bielefeld, Germany, and Sergio Scarlatti, Universitá G. D'Annunzio, Pescara, Italy
A co-publication of the AMS and Canadian Mathematical Society.
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2000; 333 pp; softcover
Volume: 28
ISBN-10: 0-8218-1959-3
ISBN-13: 978-0-8218-1959-3
List Price: US$92 Member Price: US$73.60
Order Code: CMSAMS/28

This 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.

Titles in this series are copublished with the Canadian Mathematical Society. Members of the Canadian Mathematical Society may order at the AMS member price.

Graduate students, research mathematicians, and physicists.

• F. Gesztesy, H. Holden, J. Jost, S. Paycha, M. Röckner, and S. Scarlatti -- A brief curriculum vitae of Sergio Albeverio
• F. Gesztesy, H. Holden, J. Jost, S. Paycha, M. Röckner, and S. Scarlatti -- Students and postdoctoral fellows supervised by Sergio Albeverio
• F. Gesztesy, H. Holden, J. Jost, S. Paycha, M. Röckner, and S. Scarlatti -- Publications of Sergio Albeverio
• P. Blanchard -- On the occasion of Sergio Albeverio's 60th birthday
• G. B. Arous and A. F. Ramirez -- Growth and saturation in random media
• Z. Brzeźniak and S. Peszat -- Maximal inequalities and exponential estimates for stochastic convolutions in Banach spaces
• A. M. Chebotarev and V. P. Maslov -- On Markov evolution equations in quotient probability spaces
• G. Da Prato and A. Debussche -- Maximal dissipativity of the Dirichlet operator corresponding to the Burgers equation
• G. F. Dell'Antonio, R. Figari, and A. Teta -- The Schrödinger equation with moving point interactions in three dimensions
• C. Drumond, M. de Faria, and L. Streit -- The square of self intersection local time of Brownian motion
• D. Dürr and S. Teufel -- On the role of flux in scattering theory
• E. B. Dynkin -- Probability and nonlinear analysis
• K. D. Elworthy and X.-M. Li -- Special Itô maps and an $$L^2$$ Hodge theory for one forms on path spaces
• V. Z. Enolskii, F. Gesztesy, and H. Holden -- The classical massive Thirring system revisited
• M. Fukushima -- On Ito's formulae for additive functionals of symmetric diffusion processes
• D. Hundertmark and W. Kirsch -- Spectral theory of sparse potentials
• G. Jona-Lasinio -- Invariant measures under Schrödinger evolution and quantum statistical mechanics
• Yu. G. Kondratiev, R. A. Minlos, M. Röckner, and G. V. Shchepan'uk -- Exponential mixing for classical continuous systems
• Z.-M. Ma and M. Röckner -- Diffusions on "simple" configuration spaces
• R. A. Minlos -- One- and two-particle branches of the spectrum of "many component" operators
• H. Ouerdiane and A. Rezgui -- Représentation intégrale de fonctionnelles analytiques positives
• M. Piccioni and S. Scarlatti -- Mean field models and propagation of chaos in feedforward neural networks
• M. Sanz-Solé and M. Sarrà -- Path properties of a class of Gaussian processes with applications to spde's
• B. Simon -- A Feynman-Kac formula for unbounded semigroups
• B. Zegarliński -- Hypercontractivity in non-commutative $$\bf L_p$$ spaces