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- W4319791102 abstract "We introduce the maximal correlation coefficient $R(M_1,M_2)$ between two noncommutative probability subspaces $M_1$ and $M_2$ and show that the maximal correlation coefficient between the sub-algebras generated by $s_n:=x_1+ldots +x_n$ and $s_m:=x_1+ldots +x_m$ equals $sqrt{m/n}$ for $mle n$, where $(x_i)_{iin mathbb{N}}$ is a sequence of free and identically distributed noncommutative random variables. This is the free-probability analogue of a result by Dembo--Kagan--Shepp in classical probability. As an application, we use this estimate to provide another simple proof of the monotonicity of the free entropy and free Fisher information in the free central limit theorem. Moreover, we prove that the free Stein Discrepancy introduced by Fathi and Nelson is non-increasing along the free central limit theorem." @default.
- W4319791102 created "2023-02-11" @default.
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- W4319791102 date "2020-11-05" @default.
- W4319791102 modified "2023-09-28" @default.
- W4319791102 title "Maximal correlation and monotonicity of free entropy and Stein discrepancy" @default.
- W4319791102 doi "https://doi.org/10.48550/arxiv.2011.03045" @default.
- W4319791102 hasPublicationYear "2020" @default.
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