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Motivated by the work of Fulman and Goldstein, comparing the distribution ofthe corank of random matrices in $\mathbb F_q[n]$ with the limit distributionas $n \to \infty$, we define a countdown process, driven by independentgeometric random variables related to random integer partitions. Analysis ofthis process leads to sharper bounds on the total variation distance.

A countdown process, with application to the rank of random matrices over $\mathbb F_q(n)$