András Mészáros

activity

20242026

most citedA phase transition for the cokernels of random band matrices over the p-adic integers

1 citations · 1 across the 6 of their papers we have counts for

collaborators

8 papers

math.CO2026

Persistence diagrams of random triangular matrices over finite fields

András Mészáros

Let us consider a random infinite lower triangular matrix, where the entries on and below the diagonal are i.i.d. uniform random elements of a fixed finite field. We investigate th…

math.PR2025

The persistent homology of the Linial-Meshulam process

András Mészáros

For a fixed dimension $k \geq 1$ , let us consider the randomly growing simplical complex on the vertex set ${1, 2, \dots, n}$ defined as follows: We start with the empty complex, and…

math.CO2025

Using dense graph limit theory to count cocycles of random simplicial complexes

András Mészáros

We develop a limit theory for $1$ -cochains of complete graphs with coefficients from a finite abelian group. We prove an analogue of the large deviation principle of Chatterjee and…

math.PR2025

The fluctuations of the mod p rank of triangular matrices

András Mészáros

We consider random lower triangular matrices such that the entries on and below the diagonal are i.i.d. copies of some $Z$ -valued random variable. We prove that the Sylow…

math.CO2025

The homology torsion growth of determinantal hypertrees

András Mészáros

Fix a dimension $d \geq 2$ , and let $T_{n}$ be a random $d$ -dimensional determinantal hypertree on $n$ vertices. We prove that \[\frac{\log|H_{d-1}(T_n,\mathbb{Z})|}{n\choose {d}}\] co…

math.PR2025

The rank evolution of block bidiagonal matrices over finite fields

András Mészáros

We investigate uniform random block lower bidiagonal matrices over the finite field~ $F_{q}$ , and prove that their corank undergoes a phase transition. First, we consider blo…

math.PR2024

Universal constant order fluctuations for the cokernels of block triangular matrices

András Mészáros

We prove that for a large class of random block lower triangular matrices, the Sylow $p$ -subgroups of their cokernels have the same constant order fluctuations as that of the matri…

math.PR2024★ 1 cited

A phase transition for the cokernels of random band matrices over the p-adic integers

András Mészáros

Let $B_{n}$ be an $n \times n$ Haar-uniform band matrix over $Z_{p}$ with band width $w_{n}$ . We prove that $cok (B_{n})$ has Cohen-Lenstra limiting distrib…