Author

Zhi-Peng Lu

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Preprint Sep 2026

Spectral extremes under exact cycle conditioning

Let $P_n$ be the matrix of a random permutation of $n$ symbols and let $M_n=\log\max_{|z|=1}|\det(I-zP_n)|$. Cook and Zeitouni proved that $M_n/\log n$ converges in probability to a constant $x_0$ for a uniform permutation. We show that the $\sqrt{\log n}$ fluctuations of $M_n$ are carried entirely by the number of cyc...

Zhi-Peng Lu · 0 citations

Preprint Sep 2026

Punctured adjacency-degree algebras of Cartesian products

For a connected regular graph G and a vertex a, we study the algebra generated by the adjacency and degree matrices of G-a and its cyclic module P_a generated by the all-ones vector. Our main theorem determines dim P_a for Cartesian products whose factors have equitable distance partitions at the chosen roots. A normal...

Zhi-Peng Lu · 0 citations