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

Benoît Collins; Akihiro Miyagawa

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

Functional Analysis 2025-10-23 v2 Operator Algebras

Authors: Benoît Collins , Akihiro Miyagawa

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.

Keywords

operator-valued Khintchine inequality semicircular law free probability random matrix theory adjacency matrix

Cite

@article{arxiv.2503.10558,
  title  = {Operator-valued Khintchine inequality for $\epsilon$-free semicircles},
  author = {Benoît Collins and Akihiro Miyagawa},
  journal= {arXiv preprint arXiv:2503.10558},
  year   = {2025}
}

Comments

12 pages and 1 figure. We added new bounds. This version has been accepted for publication with the Bulletin of the London Mathematical Society

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

Abstract

Keywords

Cite

Comments

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