Nicolas Privault Abstract The aim of this note is to introduce a calculus on Fock space with its probabilistic interpretations, and to give a detailed presentation of the associated quantum Itô formula. Calcul sur l’espace de Fock et une formule d’Itô non-commutative anticipante Résumé Le but de cette note est d’introduire un calcul sur l’espace de Fock et de donner une présentation détaillée d...

Looking for the universal covering of the smooth non-commutative torus leads to a curve of associative multiplications on the space O M (R) ∼= OC(R ) of Laurent Schwartz which is smooth in the deformation parameter ~. The Taylor expansion in ~ leads to the formal Moyal star product. The non-commutative torus and this version of the Heisenberg plane are examples of smooth *-algebras: smooth in t...

We show that the validity of the non-commutative Khintchine inequality for some q with 1 < q < 2 implies its validity (with another constant) for all 1 ≤ p < q. We prove this for the inequality involving the Rademacher functions, but also for more general " lacunary " sequences, or even non-commutative analogues of the Rademacher functions. For instance, we may apply it to the " Z(2)-sequences ...

This paper contains detailed proofs of our results on the moduli space and the structure of noncommutative 3-spheres. We develop the notion of central quadratic form for quadratic algebras, and a general theory which creates a bridge between noncommutative differential geometry and its purely algebraic counterpart. It allows to construct a morphism from an involutive quadratic algebras to a C*-...

It will be shown that for 1 < p < 2 the Schatten p-class is isometrically isomorphic to a subspace of the predual of a von Neumann algebra. Similar results hold for non-commutative Lp(N, τ)-spaces defined by a finite trace on a finite von Neumann algebra. The embeddings rely on a suitable notion of p-stable processes in the non-commutative setting. Introduction and Notation The theory of p-stab...

Quantum-like evolution laws for observables can be derived from classical Hamiltonian equations with the only additional assumption that the phase space is non-commutative. The derivation is possible for Hamiltonians that are polynomial functions in position and momentum variables, and supports the use of phase space distributions functions in both quantum and classical theories that rely on ex...

We present a candidate supergravity solution for a stacked configuration of stable non-BPS D-branes in Type II string theory compactified on T /Z2. This gives a supergravity description of nonabelian tachyon condensation on the brane worldvolume. BROWN-HET-1263 IC/2001/27

The Lipschitz function algebras were first defined in the 1960s by some mathematicians, including Schubert. Initially, the Lipschitz real-value and complex-value functions are defined and quantitative properties of these algebras are investigated. Over time these algebras have been studied and generalized by many mathematicians such as Cao, Zhang, Xu, Weaver, and others. Let  be a non-emp...