Central Limit Theorem for tensor products of free variables
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913336666357760 |
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| author | Lancien, Cécilia Santos, Patrick Oliveira Youssef, Pierre |
| author_facet | Lancien, Cécilia Santos, Patrick Oliveira Youssef, Pierre |
| contents | We establish a central limit theorem for tensor product random variables $c_k:=a_k \otimes a_k$, where $(a_k)_{k \in \mathbb{N}}$ is a free family of variables. We show that if the variables $a_k$ are centered, the limiting law is the semi-circle. Otherwise, the limiting law depends on the mean and variance of the variables $a_k$ and corresponds to a free interpolation between the semi-circle law and the classical convolution of two semi-circle laws. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_19662 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Central Limit Theorem for tensor products of free variables Lancien, Cécilia Santos, Patrick Oliveira Youssef, Pierre Probability Mathematical Physics Combinatorics Operator Algebras 46L54, 60F05, 47A80, 60B20 We establish a central limit theorem for tensor product random variables $c_k:=a_k \otimes a_k$, where $(a_k)_{k \in \mathbb{N}}$ is a free family of variables. We show that if the variables $a_k$ are centered, the limiting law is the semi-circle. Otherwise, the limiting law depends on the mean and variance of the variables $a_k$ and corresponds to a free interpolation between the semi-circle law and the classical convolution of two semi-circle laws. |
| title | Central Limit Theorem for tensor products of free variables |
| topic | Probability Mathematical Physics Combinatorics Operator Algebras 46L54, 60F05, 47A80, 60B20 |
| url | https://arxiv.org/abs/2404.19662 |