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arXiv · 1110.2691

An Analogue of Hin\u{c}in's Characterization of Infinite Divisibility for Operator-Valued Free Probability

John D. Williams
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Abstract

Let $B$ be a finite, separable von Neumann algebra. We prove that a $B$-valued distribution $\mu$ that is the weak limit of an infinitesimal array is infinitely divisible. The proof of this theorem utilizes the Steinitz lemma and may be adapted to provide a nonstandard proof of this type of theorem for various other probabilistic categories. We also develop weak topologies for this theory and prove the corresponding compactness and convergence results.

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John D. Williams. 2011-10-12. An Analogue of Hin\u{c}in's Characterization of Infinite Divisibility for Operator-Valued Free Probability. https://arxiv.org/abs/1110.2691

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