Roger Van Peski

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math.PR2026

Rank fluctuations of matrix products and a moment method for growing groups

Hoi H. Nguyen, Roger Van Peski

We consider the cokernel $G_{n} = Cok (A_{k} \dots A_{2} A_{1})$ of a product of independent $n \times n$ random integer matrices with iid entries from generic nondegenerate dis…

math.PR2026

The rank of a random triangular matrix over $F_{q}$

Roger Van Peski

We consider uniformly random strictly upper-triangular matrices in $Mat_{n} (F_{q})$ . For such a matrix $A_{n}$ , we show that $n-\operatorname{rank}(A_n) \approx \…

math.PR2026

Reflecting Poisson walks and dynamical universality in $p$ -adic random matrix theory

Roger Van Peski

We prove dynamical local limits for the singular numbers of $p$ -adic random matrix products at both the bulk and edge. The limit object which we construct, the reflecting Poisson s…

math.PR2025

The Gamma-disordered Aztec diamond

Maurice Duits, Roger Van Peski

We introduce a multi-parameter family of random edge weights on the Aztec diamond graph, given by certain Gamma variables, and prove several results about the corresponding random…

math.PR2025

Cohen-Lenstra flag universality for random matrix products

Yifeng Huang, Hoi H. Nguyen, Roger Van Peski

For $n \times n$ random integer matrices $M_{1}, \dots, M_{k}$ , the cokernels of the partial products $cok (M_{1} \dots M_{i}), 1 \leq i \leq k$ naturally define a random flag of a…

math.PR2025

Non-Archimedean GUE corners and Hecke modules

Jiahe Shen, Roger Van Peski

We compute the joint distribution of singular numbers for all principal corners of a $p$ -adic Hermitian (resp. alternating) matrix with additive Haar distribution, the non-archimed…

Rank fluctuations of matrix products and a moment method for growing groups

The rank of a random triangular matrix over Fq​

Reflecting Poisson walks and dynamical universality in p-adic random matrix theory

The Gamma-disordered Aztec diamond

Cohen-Lenstra flag universality for random matrix products

Non-Archimedean GUE corners and Hecke modules

The rank of a random triangular matrix over $F_{q}$

Reflecting Poisson walks and dynamical universality in $p$ -adic random matrix theory