Scattering theory for the Belavkin equation describing a quantum particle with continuously observed coordinate

In the paper, the complete investigation is given of the large times behavior of solutions of the Belavkin quantum filtering equation describing a quantum particle with continuously observed coordinate. It turns out, in particular, that these solutions have extraordinary property that can be interpreted as a sort of confinement. Namely, as t#->##infinity#, any linear combination of Gaussian wave packets will tends to a single one for almost all realizations of innovating Wiener process. In other words, several initial particles will stick together at large times, i.e. they can not be identified in the process of measurement. As a consequence, it follows that the dispersion of coordinate will always tend to the same limit, as t#->##infinity#, not depending on initial data. (orig.)Available from TIB Hannover: RO 5073(638) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Some stochastic techniques in quantization, new developments in Markov fields and quantum fields

SIGLEAvailable from Bielefeld Univ. (DE). Forschungszentrum Bielefeld-Bochum-Stochastik (BiBoS) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Construction of convergent simplicial approximations of quantum fields on Riemannian manifolds

SIGLEAvailable from Bielefeld Univ. (DE). Forschungszentrum Bielefeld-Bochum-Stochastik (BiBoS) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Maximality of infinite dimensional Dirichlet forms and Hoeegh-Krohn's model of quantum fields

SIGLEAvailable from Bochum Univ. (DE). Fakultaet fuer Mathematik / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Self-repellent random walks and polymer measures in two dimensions

SIGLECopy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

A stochastic approach to Wilson loops

Wilson loops e"i#phi#"A"("x")"d"x are investigated in two-dimensional Euclidean space-time. The electromagnetic vector potential A is regarded as a generalized random field given by the stochastic partial differential equation #delta#A = F where #delta# is a first-order differential operator and F is white noise. We give a rigorous definition of Wilson loops and examine the properties of the N-loop Schwinger functions. Key words: generalized random fields, N-loop Schwinger functions, probability measures on infinite-dimensional spaces, stochastic cosurfaces, stochastic partial differential equations, white noise, Wilson loops. (orig.)Available from TIB Hannover: RO 5073(530) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Nowhere Radon smooth measures, perturbations if Dirichlet forms and singular quadratic forms

SIGLECopy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Random walks on a p-adic tree

We construct a Markov process on the p-adic numbers, which are identified with the ends of an infinite, homogeneous tree. We compute the associated kernel by using the theory of Gelfand pairs and spherical functions on the group of isometries. We show that this process is equivalent to a random walk on p-adics, constructed by Albeverio and Karwowski (1991). (orig.)Available from FIZ Karlsruhe / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Genealogical model: evolution of population structure as p-adic dynamical system

We propose a mathematical model which described the 'global evolution' of human population. We are interested in the evolution of the genealogical structure of population, i.e. our model describes the nearness of individuals in the generalogical sense. The basic objects of this model are generalogical trees. As any mathematical model, our model is based on the idealization of real situation: we consider the ideal generalogical trees of the infinite length which contain all (possible) progency of an individual. We study the evolution processes on the configuration space of generalogical trees. To describe this evolution, we use some kind of the ergodicity postulate and reduce the time-dynamics to a dynamical system on the space of generalogical trees. It is very natural to describe genealogical trees by so-called p-adic numbers where p is the offspring parameter. Therefore, we can apply the theory of p-adic dynamical systems. We see that already the simplest nonlinear p-adic dynamical systems generate interesting behaviours of (possible) human evolution. (orig.)SIGLEAvailable from FIZ Karlsruhe / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

A remark on the support of cadlag processes

SIGLEAvailable from TIB Hannover: RO5073(498) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman