Stochastic Processes, Physics and Geometry, Volume 2; 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 Science(Conference Proceedings, Canadian Mathematical Society)

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. Members of the Canadian Mathematical Society may order at the AMS member price.

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