András Mészáros

activity

20242026

collaborators

8 papers

math.CO2026

Persistence diagrams of random triangular matrices over finite fields

AndrÃ¡s MÃ©szÃ¡ros

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.CO2026

The homology torsion growth of determinantal hypertrees

AndrÃ¡s MÃ©szÃ¡ros

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 persistent homology of the Linial-Meshulam process

AndrÃ¡s MÃ©szÃ¡ros

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.PR2025

Universal constant order fluctuations for the cokernels of block triangular matrices

AndrÃ¡s MÃ©szÃ¡ros

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.CO2025

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

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

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…