https://nci-wiki.apps.math.cnrs.fr/
2026-05-12T04:46:20+00:00
https://nci-wiki.apps.math.cnrs.fr/
https://nci-wiki.apps.math.cnrs.fr/lib/tpl/dokuwiki/images/favicon.icotext/html2023-03-09T14:27:55+00:00Anonymous (anonymous@undisclosed.example.com)bm
https://nci-wiki.apps.math.cnrs.fr/bm?rev=1678372075&do=diff
Boolean-Monotone
----------
Let $I = (S,\prec)$ be a partially ordered set.
Let $\mathcal{A}_i,~i\in I$ be a family of complex algebras indexed by $I$
Definition
We say that the algebras $\mathcal{A}_i,~i\in I$ are bm independent if the following holds:
* For all $\xi \prec \eta \succ \rho$ and $a_{\xi} \in \mathcal{A}_{\xi}, a_{\eta} \in \mathcal{A}_{\eta}, a_{\rho} \in \mathcal{A}_{\rho}$, $\varphi(a_{\xi}a_{\eta}a_{\rho})=\varphi(a_{\eta})a_{\xi}a_{\rho}$,
* For $n\geq1$, $1 \leq k\l…text/html2023-03-09T14:35:47+00:00Anonymous (anonymous@undisclosed.example.com)freeness
https://nci-wiki.apps.math.cnrs.fr/freeness?rev=1678372547&do=diff
Freeness
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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…text/html2023-03-09T14:40:05+00:00Anonymous (anonymous@undisclosed.example.com)instructions
https://nci-wiki.apps.math.cnrs.fr/instructions?rev=1678372805&do=diff
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
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First, YES, it is possible to copy/paste latex codetext/html2023-01-13T13:41:12+00:00Anonymous (anonymous@undisclosed.example.com)ref
https://nci-wiki.apps.math.cnrs.fr/ref?rev=1673617272&do=diff
@Comment{ref,
namespace = "cite"
}
@Book{GangOfFour,
author = "Erich {Gamma} and Richard {Helm} and Ralph {Johnson} and John {Vlissides}",
ref-author = "Gamma, et al.",
title = "Design Patterns: Elements of Reusable Object-Oriented Software",
publisher = "Addison-Wesley",
year = 1994,
address = "Reading, Mass.",
pages = 395,
isbn = "0-201-63361-2",
url = "http://en.wikipedia.org/wiki/Design_Patterns"
}text/html2023-01-13T13:44:14+00:00Anonymous (anonymous@undisclosed.example.com)refnotes_cite
https://nci-wiki.apps.math.cnrs.fr/refnotes_cite?rev=1673617454&do=diff
@Comment{refnotes,
namespace = "cite"
}
@article{voiculescu1987multiplication,
title={Multiplication of certain non-commuting random variables},
author={Voiculescu, Dan},
journal={Journal of Operator Theory},
pages={223--235},
year={1987},
publisher={JSTOR}
}text/html2023-01-13T13:44:53+00:00Anonymous (anonymous@undisclosed.example.com)refnotes
https://nci-wiki.apps.math.cnrs.fr/refnotes?rev=1673617493&do=diff
@Comment{refnotes,
namespace = "cite"
}
@article{voiculescu1987multiplication,
title={Multiplication of certain non-commuting random variables},
author={Voiculescu, Dan},
journal={Journal of Operator Theory},
pages={223--235},
year={1987},
publisher={JSTOR}
}text/html2023-03-09T14:40:42+00:00Anonymous (anonymous@undisclosed.example.com)sidebar
https://nci-wiki.apps.math.cnrs.fr/sidebar?rev=1678372842&do=diff
* Independences on algebras
* Muraki's Five
* Voiculescu's Freeness
* Mixtures
* Boolean-Monotone
* Multi-states
* Cyclic independences
* Multi-faced
* Positive
* Others
* Traffictext/html2023-03-09T15:09:50+00:00Anonymous (anonymous@undisclosed.example.com)start
https://nci-wiki.apps.math.cnrs.fr/start?rev=1678374590&do=diff
Non-commutative independences
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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$