Rates of Convergence in the Free Central Limit Theorem
Copyright policy )Rates of Convergence in the Free Central Limit Theorem
We study the free central limit theorem for not necessarily identically distributed free random variables where the limiting distribution is the semicircle distribution. Starting from an estimate for the Kolmogorov distance between the measure of suitably normalized sums of free random variables and the semicircle distribution without any moment condition, we show the free Lindeberg central limit theorem and improve the known results on rates of convergence under the conditions of the existence of the third moments.
7 page
- Nagoya City University Japan
- Keio University
- Keio University Japan
Free probability and free operator algebras, Probability (math.PR), central limit theorem, FOS: Mathematics, Central limit and other weak theorems, free probability, Mathematics - Probability, rate of convergence
Free probability and free operator algebras, Probability (math.PR), central limit theorem, FOS: Mathematics, Central limit and other weak theorems, free probability, Mathematics - Probability, rate of convergence
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