Work

The fluctuations of the mod p rank of triangular matrices

Year: 2026

Type: article

Abstract: We consider random lower triangular matrices such that the entries on and below the diagonal are i.i.d. copies of some dollar sign double struck upper Z dollar sign $\mathbb{Z}$ $ ℤ $ -valued random variable. We prove that the Sylow dollar sign p dollar sign $p$ $ p $ -subgroups of the cokernels of these matrices have the same constant order fluctuations as those of the matrix products studied by Nguyen and Van Peski. Unlike for matrix products, for triangular matrices, the law of the limiting fluctuations depends slightly on the distribution of the entries. As a special case, we can describe the limiting fluctuations of the rank of lower triangular matrices over dollar sign double struck upper F p dollar sign $\mathbb{F}_p$ $ 𝔽 p $ with i.i.d. random entries on and below the diagonal.

Source: Proceedings of the Royal Society of Edinburgh Section A Mathematics

DOI: 10.1017/prm.2026.10158

Author: András Mészáros

Institutions: HUN-REN Alfréd Rényi Institute of Mathematics, Hungarian Research Network

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

OpenAlex ID: W4416243746

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