9 papers · 1 filter
Sharp Threshold for Universality of Rational Canonical Forms over a Finite Field
Jiahe Shen
We study the rational canonical form of sparse random matrices over a finite field. Suppose has independent and -balanced entries.…
The Resultant Distribution Method: Universality for -adic Random Matrices and Polynomials
Jiahe Shen
We prove universality of limiting local eigenvalue statistics for random matrices over . In previous work of the author and Van Peski (arXiv:2601.06283), the limiting…
Hitting time mixing for random -cycles
Chen Shang, Jiahe Shen, Jiyue Zeng +1
In this paper, we study the random walk on the symmetric group generated by the conjugacy class of -cycles, where . We prove that the wa…
The Cutoff Profile for Random Transpositions on Repeated Cards in the Full Range of Parameters
Jiahe Shen
The random transposition shuffle on repeated cards induces a Markov chain on the quotient space of arrangements with multiplicities, and is equivalent to the many-urn mean-field Be…
The -cycle shuffling with repeated cards
Jiahe Shen
We investigate the -cycle shuffle on repeated cards, namely on a deck consisting of identical copies of each of card types, with total size . We establish asymptot…
Quantative universality for cokernels of matrices with symmetries
Jiahe Shen
We prove universality for cokernels of random integral matrices with symmetries via an approach different from the classical surjection moment method introduced by Wood (arXiv:1402…