Distributional comparison for non-commutative infinitely divisible probability measures

Arturo Jaramillo; Josue Vazquez-Becerra

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arXiv · 2606.30364

Distributional comparison for non-commutative infinitely divisible probability measures

Arturo Jaramillo·Josue Vazquez-Becerra

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Abstract

We determine ``cumulant-type'' upper bounds of the non-commutative Wasserstein distance for certain classes of distributions $\mu$ and $\nu$, which are infinite divisible with respect to the Boolean, classical and free convolutions. The main contribution of the manuscript is an estimation of the non-commutative Wasserstein distance between $\mu$ and $\nu$, expressed in terms of the difference between cumulants of order less than $2m+4$.

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Arturo Jaramillo, Josue Vazquez-Becerra. 2026-06-29. Distributional comparison for non-commutative infinitely divisible probability measures. https://arxiv.org/abs/2606.30364

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