András Mészáros

collaborators

5 papers

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.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 rank undergoes a phase transition. First, we consider block…

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…