In this paper a systematic study of Markov dilations is begun for completely positive
operators on W∗-algebras which leave a faithful normal state invariant. It is shown that a …

A class of non-commutative stochastic processes is defined. These processes are defined
up to equivalence by their multi-time correlation kernels. A reconstruction theorem …

Conditional expectations play an important role in classical probability theory. In the general
context of von Neumann algebras they were impliciteiy used by von Neumann [41, Chap. II] …

We provide a rigorous lattice approximation of conformal field theories given in terms of
lattice fermions in 1+ 1-dimensions, focussing on free fermion models and Wess–Zumino …

We present a theory of non-commutative stochastic integration analogous to the Itô-theory. It
is shown that Wick products of Fermi fields define martingales and that stochastic integrals …

For identity and trace preserving one-parameter semigroups T tt≧ 0 on the n× n-matrices M
n we obtain a complete description of their “essentially commutative” dilations, ie, dilations …

It is known that determinantal point processes have an intimate relation to operator algebras.
In the paper, we extend this relationship to encompass dynamical aspects. Especially, we …

We consider pure fermionic states with a varying number of quasiparticles and analyze two
types of reduced density operators: one is obtained via tracing out modes, the other is …

A theory of quantum martingales and quantum stochastic integrals in quasi-free
representations of the CAR and CCR is presented. For the CAR, the results generalize some …

The purpose of this volume is to give a detailed account of a series of re sults concerning
some ergodic questions of quantum mechanics which have the past six years following the …