In this paper, we study the superconvergence phenomenon in the free central limit theorem for identically distributed, unbounded summands. We prove not only the uniform convergence of the densities to the semicircular density but also their Lp-convergence to the same limit for p > 1/2. Moreover, an entropic central limit theorem is obtained as a consequence of the above results.
Publié le : 2010-07-15
Classification:
Free central limit theorem,
superconvergence,
local limit theorems,
free entropy,
46L54,
60F05,
60F25
@article{1278593957,
author = {Wang, Jiun-Chau},
title = {Local limit theorems in free probability theory},
journal = {Ann. Probab.},
volume = {38},
number = {1},
year = {2010},
pages = { 1492-1506},
language = {en},
url = {http://dml.mathdoc.fr/item/1278593957}
}
Wang, Jiun-Chau. Local limit theorems in free probability theory. Ann. Probab., Tome 38 (2010) no. 1, pp. 1492-1506. http://gdmltest.u-ga.fr/item/1278593957/