On the second moment of the determinant of random symmetric, Wigner, and Hermitian matrices

Dominik Beck; Zelin Lv; Aaron Potechin

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arXiv · 2409.14620

On the second moment of the determinant of random symmetric, Wigner, and Hermitian matrices

Dominik Beck·Zelin Lv·Aaron Potechin

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Abstract

In this paper, we analyze the second moment of the determinant of random symmetric, Wigner, and Hermitian matrices. Using analytic combinatorics techniques, we determine the second moment of the determinant of Hermitian matrices whose entries on the diagonal are i.i.d and whose entries above the diagonal are i.i.d. and have real expected values. Our results extend previous work analyzing the second moment of the determinant of symmetric and Wigner matrices, providing a unified approach for this analysis.

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Dominik Beck, Zelin Lv, Aaron Potechin. 2024-09-22. On the second moment of the determinant of random symmetric, Wigner, and Hermitian matrices. https://arxiv.org/abs/2409.14620

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