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

Published 22 Jun 2024 in math.OA, math.FA, and math.RA | (2406.15922v1)

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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