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arXiv · 2306.16679

A short note on strong convergence of $q$-Gaussians

Akihiro Miyagawa
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Abstract

In this note, we prove strong convergence of $q$-Gaussians with respect to a parameter $q$, which implies the spectrum of any self-adjoint non-commutative polynomial in $q$-Gaussians is continuously deformed with respect to $q$. With Bo\.{z}ejko's Haagerup-type inequality, we follow Brannan's approach to proving the asymptotic strong convergence of the free orthogonal quantum group.

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Akihiro Miyagawa. 2023-06-29. A short note on strong convergence of $q$-Gaussians. https://arxiv.org/abs/2306.16679

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