Roger Van Peski

collaborators

10 papers

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.CO2026

Groups with pairings, Hall modules, and Hall-Littlewood polynomials

Jiahe Shen, Roger Van Peski

We relate the combinatorics of Hall-Littlewood polynomials to that of abelian $p$ -groups with alternating or Hermitian perfect pairings. Our main result is an analogue of the class…

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.CO2026

Symmetric functions and the explicit moment problem for abelian groups

Roger Van Peski

Recently, Sawin and Wood (arXiv:math/2210.06279) proved a formula for the distribution of a random abelian group $G$ in terms of its $H$ -moments $\mathbb{E} [\#\operatorname{Sur}(G…

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.NT2026

Eigenvalues of $p$ -adic random matrices

Jiahe Shen, Roger Van Peski

We develop the basic theory of eigenvalues of $p$ -adic random matrices, analogous to the classical theory for random matrices over $R$ and $C$ . Such eigenvalue st…

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

Groups with pairings, Hall modules, and Hall-Littlewood polynomials

The rank of a random triangular matrix over Fq​

Symmetric functions and the explicit moment problem for abelian groups

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

Eigenvalues of p-adic random matrices

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

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

Eigenvalues of $p$ -adic random matrices