Cohen–Lenstra conjecture for the largest torsion group in random complexes

Let $LT(n)$ be the largest torsion group found in the first homology during the torsion burst of the Linial–Meshulam process. For a fixed prime $q$, let the Sylow $q$-subgroup of $LT(n)$ be the maximal subgroup of order a power of $q$. Cohen–Lenstra conjecture for $LT(n)$. For a fixed prime $q$, the Sylow $q$-subgroup of $LT(n)$ is asymptotically distributed according to the Cohen–Lenstra distribution, which assigns probability

$$\frac{\prod_{k=1}^{\infty}(1-q^{-k})}{|\operatorname{Aut}(G)|}$$

to any finite abelian $q$-group $G$. This is motivated by analogous models of random abelian groups and supported in the paper by computational experiments; the asserted limiting distribution remains conjectural.