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arXiv · 2303.13926

On the free L\'{e}vy measure of the normal distribution

Takahiro Hasebe·Yuki Ueda
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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.

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Takahiro Hasebe, Yuki Ueda. 2023-03-24. On the free L\'{e}vy measure of the normal distribution. https://arxiv.org/abs/2303.13926

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