A countdown process, with application to the rank of random matrices   over $\mathbb F_q(n)$
  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. 
Richard Arratia and Michael Earnest
math.PR math.CO