An extension of a non-commutative Choquet-Deny theorem

A Non-commutative Bertini Theorem

We prove a version of the classical ‘generic smoothness’ theorem with smooth varieties replaced by non-commutative resolutions of singular varieties. This in particular implies a non-commutative version of the Bertini theorem.

An extension of the Wedderburn-Artin Theorem

‎In this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.

A Non-commutative Extension of MELL

We extend multiplicative exponential linear logic (MELL) by a non-commutative, self-dual logical operator. The extended system, called NEL, is defined in the formalism of the calculus of structures, which is a generalisation of the sequent calculus and provides a more refined analysis of proofs. We should then be able to extend the range of applications of MELL, by modelling a broad notion of s...

Strongly Approximately Transitive Group Actions, the Choquet-deny Theorem, and Polynomial Growth

A non-commutative Lévy-Cramér continuity theorem

The classical Lévy-Cramér continuity theorem asserts that the convergence of the characteristic functions implies the weak convergence of the corresponding probability measures. We extend this result to the setting of non-commutative probability theory and discuss some applications. ∗CNRS, Université de Provence, Université de la Méditerranée, Université du Sud Toulon-Var. 2 V. Jakšić, Y. Pautr...