<p>The Cohen-Lenstra heuristic predicts the distribution of ideal class groups over number fields. Random matrix models provide a natural framework for explaining this heuristic, and recent results demonstrate the effectiveness of these tools. In this paper, we extend the analysis of the random matrix model to examine the error term in the Cohen-Lenstra heuristic. Additionally, we derive the asymptotic distribution of the corank of random matrices over finite fields, which can be modeled as a special class of Markov chains.</p>