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arXiv · 2406.15922

Fuglede-Kadison determinants of matrix-valued semicircular elements and capacity estimates

Tobias Mai·Roland Speicher
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Abstract

We calculate the Fuglede-Kadison determinant of arbitrary matrix-valued semicircular operators in terms of the capacity of the corresponding covariance mapping. We also improve a lower bound by Garg, Gurvits, Oliveira, and Widgerson on this capacity, by making it dimension-independent.

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Tobias Mai, Roland Speicher. 2024-06-22. Fuglede-Kadison determinants of matrix-valued semicircular elements and capacity estimates. https://arxiv.org/abs/2406.15922

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