Berry-Esseen for Free Random Variables
Vladislav Kargin
Abstract
An analogue of the Berry-Esseen inequality is proved for the speed of convergence of free additive convolutions of bounded probability measures. The obtained rate of convergence is of the order n-1/2, the same as in the classical case. An example with binomial measures shows that this estimate cannot be improved without imposing further restrictions on convolved measures.
Create a lesson
Related papers
Shannon's problem on the monotonicity of entropy and a Conjecture of Tao
Ziran Liu
Extinction, Survival and Fluctuations for the Spatial Maki--Thompson Model on Infinite Graphs
Luciano Henrique Lacerda de Araújo, Daniel Miranda Machado, Cristian Favio Coletti et al.
Phase Transition and Fluctuation Results for First-Passage Percolation on Spread-Out Cycle Graphs
Partha S. Dey, Daecheol Kim
Colorful Exponential Random Graph Models
Bhaswar B. Bhattacharya, Pierfrancesco Dionigi, Ankan Ganguly et al.
On (fake) Stationarity in Stochastic Volterra Equations with Affine Drift and Regular Kernels
Emmanuel Gnabeyeu, Gilles Pagès
Limit Laws of the Iterated Logarithm Under Sub-linear Expectations
Li-Xin Zhang, Yongsheng Song