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- W4313331867 abstract "Several results giving upper bounds for the speed of convergence in non-commutative central limit theorems are known. A natural question is whether there also exist lower bounds, or whether there exist classes of probability measures where the speed of convergence is faster. In this paper, we answer this for the Boolean central limit theorem in the bounded support case and using the Lévy distance. We show that for a probability measure [Formula: see text] of bounded support and nonzero third moment the rate of convergence is at least [Formula: see text], and when we have zero third moment, then the rate of convergence is [Formula: see text]. To achieve this, we improve a previous result concerning the position and weights of two atoms that eventually appear in the converging measure. The proofs only require elementary techniques of complex analysis." @default.
- W4313331867 created "2023-01-06" @default.
- W4313331867 creator A5084414081 @default.
- W4313331867 date "2023-03-01" @default.
- W4313331867 modified "2023-09-26" @default.
- W4313331867 title "A note on the rate of convergence in the Boolean central limit theorem" @default.
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- W4313331867 doi "https://doi.org/10.1142/s0219025722500321" @default.
- W4313331867 hasPublicationYear "2023" @default.
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