freeness
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freeness [2023/01/13 13:45] – [Models] ngilliers | freeness [2023/03/09 14:35] (current) – ngilliers | ||
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- | ======== Freeness ======== | + | ========= Freeness ========= |
+ | ---- | ||
- | ===== Definition | + | <typo font-size: |
+ | </ | ||
- | **Definition** [Freeness [(: | ||
- | ] | ||
Let $\mathcal{A}$ be a unital complex algebra equipped with a linear functional $\psi: | Let $\mathcal{A}$ be a unital complex algebra equipped with a linear functional $\psi: | ||
\psi(a_1\cdots a_n) = 0.$$ | \psi(a_1\cdots a_n) = 0.$$ | ||
- | ===== Models ====== | ||
- | Here[(: | + | ===== - Models ===== |
- | ** Theorem ** | ||
- | Let $R> | + | |
+ | |||
+ | Let $R > 0$ a real number. For each $N\geq 1$, let $U_N$ be a Haar distributed unitary random matrix. Then, for any $P\in \mathbb{C}\langle X_k, | ||
freeness.1673617513.txt.gz · Last modified: 2023/01/13 13:45 by ngilliers