András Mészáros

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20242026

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5 papers · 1 filter

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.PR2025

The fluctuations of the mod p rank of triangular matrices

AndrÃ¡s MÃ©szÃ¡ros

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

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

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

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…