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arXiv · 2606.05430

On a random matrix proof of a bipartite Harer-Zagier formula

Guillaume Dubach·Hai An Mai
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Abstract

This work establishes a bipartite generalization of the Harer-Zagier formula using non-Hermitian Random Matrix Theory. More specifically, we use a decomposition of powers of Ginibre eigenvalues as a superposition of independent point processes to identify all coefficients of the generating function of the genus of a surface obtained by a random bipartite pairing of the sides of one polygon with $kM$ sides and $k$ polygons with $M$ sides.

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Guillaume Dubach, Hai An Mai. 2026-06-03. On a random matrix proof of a bipartite Harer-Zagier formula. https://arxiv.org/abs/2606.05430

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