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- W2964124055 abstract "Let {T k } ∞ k=1 be a family of *-free identically distributed operators in a finite von Neumann algebra. In this work we prove a multiplicative version of the Free Central Limit Theorem. More precisely, let B n = T 1 * T 2 * ... T n * T n ... T 2 T 1 ; then B n is a positive operator and B n 1/2n converges in distribution to an operator A. We completely determine the probability distribution ν of ∧ from the distribution μ of |T| 2 . This gives us a natural map G: M + → M + with μ → G(μ) = ν. We study how this map behaves with respect to additive and multiplicative free convolution. As an interesting consequence of our results, we illustrate the relation between the probability distribution ν and the distribution of the Lyapunov exponents for the sequence {T k } ∞ k=1 introduced in [12]." @default.
- W2964124055 created "2019-07-30" @default.
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- W2964124055 date "2010-01-01" @default.
- W2964124055 modified "2023-09-29" @default.
- W2964124055 title "Limits laws for geometric means of free random variables" @default.
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- W2964124055 doi "https://doi.org/10.1512/iumj.2010.59.3775" @default.
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