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arXiv · 2512.24720

Products of random Hermitian matrices and brickwork Hurwitz numbers. Products of normal matrices

Ch. Li·A. Yu. Orlov
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Abstract

We consider products of $n$ random Hermitian matrices which generalize the one-matrix model and show its relation to Hurwitz numbers which count ramified coverings of certain type. Namely, these Hurwitz numbers count $2k$-fold ramified coverings of the Riemann sphere with arbitrary ramification type over $0$ and $\infty$ and ramifications related to the partition $(2^k)$ (``brickworks'' - involution without fixed points) elsewhere. Products of normal random matrices are also considered.

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Ch. Li, A. Yu. Orlov. 2025-12-31. Products of random Hermitian matrices and brickwork Hurwitz numbers. Products of normal matrices. https://arxiv.org/abs/2512.24720

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