A countdown process, with application to the rank of random matrices over ${\mathbb{F}}_q(n)$

Abstract

Motivated by the work of Fulman and Goldstein, comparing the distribution of the corank of random matrices in ${\mathbb{F}}_q[n]$ with the limit distribution as $n\to \infty$, we define a countdown process, driven by independent geometric random variables related to random integer partitions. Analysis of this process leads to sharper bounds on the total variation distance.