Quantum probability and infinite dimensional analysis : proceedings of the Conference Quantum Probability and Infinite Dimensional Analysis : Burg (Spreewald), Germany, 15-20 March, 2001

Fred Almgren created the excess method for proving regularity theorems in the calculus of variations. His techniques yielded Holder continuity except for a small closed singular set. In the sixties and seventies Almgren refined and generalized his methods. Between 1974 and 1984 he wrote a 1,700-page proof that was his most ambitious exposition of his ground-breaking ideas. Originally, this monograph was available only as a three-volume work of limited circulation. The entire text is faithfully reproduced here.This book gives a complete proof of the interior regularity of an area-minimizing rectifiable current up to Hausdorff codimension 2. The argument uses the theory of Q-valued functions, which is developed in detail. For example, this work shows how first variation estimates from squash and squeeze deformations yield a monotonicity theorem for the normalized frequency of oscillation of a Q-valued function that minimizes a generalized Dirichlet integral. The principal features of the book include an extension theorem analogous to Kirszbraun's theorem and theorems on the approximation in mass of nearly flat mass-minimizing rectifiable currents by graphs and images of Lipschitz Q-valued functions Markov property - recent developments on the quantum Markov property, L. Accardi and F. Fidaleo; stationary quantum stochastic processes from the cohomological point-of-view, G.G. Amosov; the Feller property of a class of quantum Markov semigroups II, R. Carbone and F. Fagnola; recognition and teleportation, K.-H. Fichtner et al; prediction errors and completely positive maps, R. Gohm; multiplicative properties of double stochastic product integrals, R.L. Hudson; isometric cocycles related to beam splittings, V. Liebscher; multiplicativity via a hat trick, J.M. Lindsay and S.J. Wills; dilation theory and continuous tensor product systems of Hilbert modules, M. Skeide; quasi-free fermion planar quantum stochastic integrals, W.J. Spring and I.F. Wilde. (Part contents) This volume consists of 18 research papers reflecting the impressive progress made in the field of quantum probability and infinite-dimensional analysis. It includes results on quantum stochastic integration, the stochastic limit, quantum teleportation, and other areas. This volume consists of 18 research papers reflecting the impressive progress made in the field. It includes new results on quantum stochastic integration, quantum Markov processes, the stochastic limit, quantum teleportation and other areas.