BMT Independence

2023/09/08 by Arizmendi, Octavio, Mendoza, Saul Rogelio, Vazquez-Becerra, Josué · 2 citations
#46L54 #FOS: Mathematics #Operator Algebras (math.OA) #Probability (math.PR)

paper · doi:10.48550/arxiv.2309.04123

Abstract

We introduce the notion of BMT independence, allowing us to take arbitrary mixtures of boolean, monotone, and tensor independence and generalizing the notion of BM independence of Wysoczanski. Pair-wise independence relations are encoded through a directed graph, which in turn determines the way mixed moments must be computed. Corresponding Central and Poisson-Type Limit Theorems are provided along with an explicit construction to realize BMT independent random variables as bounded operators on certain Hilbert space.

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• Monotone max-convolution and subordination functions for free max-convolution
• Scaling limit theorem for mixed free and Boolean convolution powers

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