Cohen–Lenstra distribution conjecture for torsion homology of random simplicial complexes

Let $X_\bullet$ be a random simplicial complex, and let $H_\ast(X_\bullet)_{\operatorname{tors}}$ denote the torsion subgroup of its homology. A Cohen–Lenstra distribution conjecture. Does $H_\ast(X_\bullet)_{\operatorname{tors}}$ have a Cohen–Lenstra distribution? This asks whether the Cohen–Lenstra heuristics for random algebraic objects extend to torsion homology of random topological objects; the source poses it as a problem without stating a resolution.