A non-commutative Bayes' 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.

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...

Non-commutative Extensions of the Macmahon Master Theorem

We present several non-commutative extensions of the MacMahon Master Theorem, further extending the results of Cartier-Foata and Garoufalidis-LêZeilberger. The proofs are combinatorial and new even in the classical cases. We also give applications to the β-extension and Krattenthaler-Schlosser’s q-analogue. Introduction The MacMahon Master Theorem is one of the jewels in enumerative combinatori...

Convergence Theorem for Non-commutative Feynman Graphs and Renormalization

We present a rigorous proof of the convergence theorem for the Feynman graphs in arbitrary massive Euclidean quantum field theories on non-commutative R (NQFT). We give a detailed classification of divergent graphs in some massive NQFT and demonstrate the renormalizability of some of these theories. E-mail: [email protected] 2 E-mail: [email protected]

Serre-Swan Theorem for non commutative C∗-algebras