Universal constant order fluctuations for the cokernels of block triangular matrices

TL;DR

This paper demonstrates that for a broad class of random block lower triangular matrices, the fluctuations of their cokernels' Sylow p-subgroups follow a universal constant order pattern, extending previous results to more general conditions.

Contribution

It generalizes the known fluctuation results of cokernels to a wider class of matrices and weakens the assumptions needed for these universal behaviors.

Findings

Cokernels' Sylow p-subgroups exhibit universal constant order fluctuations.

The results apply to a larger class of matrices than previously studied.

The theorem holds under weaker assumptions on matrix product factors.

Abstract

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 matrix products studied by Nguyen and Van Peski in arXiv:2409.03099. We also show that the theorem of Nguyen and Van Peski remains true under a weaker assumption on the number of factors in the matrix products.