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arXiv · 2503.10558

Operator-valued Khintchine inequality for $\epsilon$-free semicircles

Benoît Collins·Akihiro Miyagawa
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Abstract

We exhibit several bounds for operator norms of the sum of $\epsilon$-free semicircular random variables introduced in the paper of Speicher and Wysocza\'{n}ski. In particular, using the first and second largest eigenvalues of the adjacency matrix $\epsilon$, we show analogs of the operator-valued Khintchine-type inequality obtained by Haagerup and Pisier.

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Benoît Collins, Akihiro Miyagawa. 2025-03-13. Operator-valued Khintchine inequality for $\epsilon$-free semicircles. https://arxiv.org/abs/2503.10558

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