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Stochastic Processes, Physics and Geometry: New Interplays. II: 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; 647 pp; softcover
Volume: 29
ISBN-10: 0-8218-1960-7
ISBN-13: 978-0-8218-1960-9
List Price: US$145 Member Price: US$116
Order Code: CMSAMS/29

This volume and Stochastic Processes, Physics and Geometry: New Interplays. I 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.

• V. Adamyan and B. Pavlov -- Valuation of bonds and options under floating interest rate
• I. Ya. Aref'eva and I. V. Volovich -- The large time behaviour in quantum field theory and quantum chaos
• L. V. Bogachev, S. A. Molchanov, Yu. A. Makhnovskii, and A. M. Berezhkovskii -- Correlation effects in the trapping problem: General approach and rigorous results
• B. Booss-Bavnbek -- Boundary reduction of spectral invariants-Results and puzzles
• S. Borac and R. Seiler -- Loop group factorization of biorthogonal wavelet bases
• J. F. Brasche, M. M. Malamud, and H. Neidhardt -- Weyl functions and singular continuous spectra of self-adjoint extensions
• J. Brüning -- Irregular spectral asymptotics
• L. Cattaneo and U. Cattaneo -- The Lagrangian gauge problem in classical mechanics and group cohomology
• F. Cipriani -- Perron theory for positive maps and semigroups on von Neumann algebras
• Ph. Clément, G. Gripenberg, and V. Högnäs -- Some remarks on the method of sums
• M. Demuth -- Stochastic processes and the spectrum of Feller operators
• B. K. Driver and B. C. Hall -- The energy representation has no non-zero fixed vectors
• G. G. Emch and A. Z. Jadczyk -- Weakly projective representations, quaternions, and monopoles
• P. Exner -- Point interactions in a tube
• R. Fan and K. Lange -- Asymptotic properties of the maximal subinterval of a Poisson process
• F. Figliolini and D. Guido -- Inclusions of second quantization algebras
• L. Gawarecki and V. Mandrekar -- Weak solutions to stochastic differential equations with discontinuous drift in Hilbert space
• F. Gesztesy, K. A. Makarov, and A. K. Motovilov -- Monotonicity and concavity properties of the spectral shift function
• V. A. Geyler and V. A. Margulis -- Zero-range perturbations of the Schrödinger operator with a saddle-point potential
• R. Gielerak and P. Ługiewicz -- 4D gauge-like quantum fields from rectangular systems of stochastic partial differential equations
• G. A. Goldin and U. Moschella -- Generalized configuration spaces for quantum systems
• K. Gustafson -- A composition adjoint lemma
• K. Habermann -- An $$M_p^{\mathbb C}$$-spinorial approach to a geometric-type quantization for symplectic manifolds
• A. Hilbert and R. Léandre -- Nagel-Stein-Wainger estimates for balls associated with the Bismut condition
• F. Hiroshima -- Euclidean Gell-Mann-Low formula and double stochastic integrals
• H. Holden, K. H. Karlsen, and K.-A. Lie -- Operator splitting methods for degenerate convection-diffusion equations I: Convergence and entropy estimates
• Y. Hu -- A class of SPDE driven by fractional white noise
• Y. Hu, B. Øksendal, and T. Zhang -- Stochastic partial differential equations driven by multiparameter fractional white noise
• P. Imkeller -- Some support properties of the laws of invariant spaces of stochastic differential equations
• G. W. Johnson and L. Nielsen -- A stability theorem for Feynman's operational calculus
• N. A. Kachanovsky -- On a biorthogonal approach to the construction of non-Gaussian analysis
• G. Karner -- Twist maps, kicked rotors, and quantum chaos
• W. Karwowski and V. Koshmanenko -- The generalized Laplace operator in $$L_2(\mathbb R^n)$$
• A. Khrennikov and B. Tirozzi -- Learning of $$p$$-adic neural networks
• Y. Kozitsky -- Quantum effects in lattice models of vector anharmonic oscillators
• P. Kurasov and K. Watanabe -- On rank one $$H_{\_3}$$-perturbations of positive self-adjoint operators
• K. Kuwae -- On a strong maximum principle for Dirichlet forms
• B.-H. Li and Y.-Q. Li -- On the relation between the model product and the harmonic product of distributions
• X. D. Li -- Sobolev spaces and capacity theory on path spaces
• V. Liebscher -- Integration by parts formulae for point processes
• J. M. Lindsay and S. J. Wills -- Fock space Markovian cocycles: Their representation, generation, and dilation
• I. Mitoma -- Wiener space approach to a perturbative Chern-Simons integral
• L. M. Morato -- From Nelson's kinematics to symmetric and non symmetric ground-state transformations
• G. Morchio and F. Strocchi -- Representations of *-algebras in indefinite inner product spaces
• D. Noja and A. Posilicano -- Delta interactions and electrodynamics of point particles
• N. Obata -- Coherent state representations in white noise calculus
• Y. Oshima -- Certain ratio limit theorem for time inhomogeneous Markov chains
• H. Osswald -- Infinitesimals in abstract Wiener spaces
• G. Panati and A. Teta -- The flux-across-surfaces theorem for a point interaction Hamiltonian
• B. Rüdiger and J.-L. Wu -- Construction by subordination of processes with jumps on infinite dimensional state spaces and corresponding non local Dirichlet forms
• A. Sergeev -- Diff$$_+(S^1)/S^1$$ as a space of complex structures on loop spaces of compact Lie groups
• O. G. Smolyanov, H. v. Weizsäcker, and O. Wittich -- Brownian motion on a manifold as limit of stepwise conditioned standard Brownian motions
• R. F. Streater -- The analytic quantum information manifold
• M. Takeda -- $$L^p$$-independence of the spectral radius of symmetric Markov semigroups
• M. Zähle -- Measure theoretic Laplace operators on fractals
• W. Zheng -- Estimation of the phase transition time in the Stefan problem
• W. Zhengdong -- Cocycles of loop groups