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Central Limit Theorem for tensor products of free variables
- Part of
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- Journal:
- Canadian Journal of Mathematics , First View
- Published online by Cambridge University Press:
- 16 December 2024, pp. 1-33
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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.
