start

ngilliers (ngilliers@undisclosed.example.com) — 2023-03-09T15:09:50+00:00

Non-commutative independences ---------- This is a wiki dedicated to non-commutative independences. The objective is to build a catalog with a few informations about each of them and bibliographical references. I am listing here some non-commutative independences I am aware of (NG writing). Of course, do not hesitate to add to the list those missings, even if you do not have time/energy to write an entry about it.$\Lambda$$\varepsilon$$\Lambda$$O$

sidebar

ngilliers (ngilliers@undisclosed.example.com) — 2023-03-09T14:40:42+00:00

* Independences on algebras * Muraki's Five * Voiculescu's Freeness * Mixtures * Boolean-Monotone * Multi-states * Cyclic independences * Multi-faced * Positive * Others * Traffic

instructions - [1.1 Models]

ngilliers (ngilliers@undisclosed.example.com) — 2023-03-09T14:40:05+00:00

Some instructions about writing an entry and adding bibliography. I think some of you are familiar with the mathematics for the web, and for those people everything work as usual General Comments ---------- First, YES, it is possible to copy/paste latex code

freeness

ngilliers (ngilliers@undisclosed.example.com) — 2023-03-09T14:35:47+00:00

Freeness ---------- Definition Dan Voiculescu, 1987. Multiplication of certain non-commuting random variables. Journal of Operator Theory, JSTOR, pp.223--235. Let $\mathcal{A}$ be a unital complex algebra equipped with a linear functional $\psi:\mathcal{A}\to \mathbb{C}$ where $\psi$ is unital. Let $\mathcal{A}_1 ,\mathcal{A}_2 \subset \mathcal{A}$$\mathcal{A}_1$$\mathcal{A}_2$$\psi$$(a_1,\ldots,a_n)$$\mathcal{A}_1\cup \mathcal{A}_2$$\psi$$$\label{eqn:freemoments} \psi(a_1\cdots a_n) = 0…

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