On the free L\'{e}vy measure of the normal distribution
Probability
2023-10-16 v3 Operator Algebras
Abstract
Belinschi et al. [Adv. Math., 226 (2011), 3677--3698] proved that the normal distribution is freely infinitely divisible. This paper establishes a certain monotonicity, real analyticity and asymptotic behavior of the density of the free L\'{e}vy measure. The monotonicity property strengthens the result in Hasebe et al. [Int. Math. Res. Not. (2019), 1758--1787] that the normal distribution is freely selfdecomposable.
Keywords
Cite
@article{arxiv.2303.13926,
title = {On the free L\'{e}vy measure of the normal distribution},
author = {Takahiro Hasebe and Yuki Ueda},
journal= {arXiv preprint arXiv:2303.13926},
year = {2023}
}
Comments
18 pages, 6 figures