Distribution of the cokernels of determinantal row-sparse matrices

Jungin Lee; Myungjun Yu

paper

Distribution of the cokernels of determinantal row-sparse matrices

arXiv:2505.11700

Abstract

We study the distribution of the cokernels of random row-sparse integral matrices $A_{n}$ according to the determinantal measure from a structured matrix $B_{n}$ with a parameter $k_{n} \geq 3$ . Under a mild assumption on the growth rate of $k_{n}$ , we prove that the distribution of the $p$ -Sylow subgroup of the cokernel of $A_{n}$ converges to that of Cohen--Lenstra for every prime $p$ . Our result extends the work of A. Mészáros which established convergence to the Cohen--Lenstra distribution when $p \geq 5$ and $k_{n} = 3$ for all positive integers $n$ .

arXiv comment26 pages, to appear in Israel J. Math