We study torsion in homology of the random d-complex Y ∼ Y d (n, p) experimentally. Our experiments suggest that there is almost always a moment in the process where there is an enormous burst of torsion in homology H d−1 (Y ). This moment seems to coincide with the phase transition studied in [1,20,21] , where cycles in H d (Y ) first appear with high probability.Our main study is the limiting distribution on the q-part of the torsion subgroup of H d−1 (Y ) for small primes q. We find strong evidence for a limiting Cohen-Lenstra distribution, where the probability that the q-part is isomorphic to a given q-group H is inversely proportional to the order of the automorphism group |Aut(H)|.We also study the torsion in homology of the uniform random Q-acyclic 2-complex. This model is analogous to a uniform spanning tree on a complete graph, but more complicated topologically since Kalai showed that the expected order of the torsion group is exponentially large in n 2 [14]. We give experimental evidence that in this model also, the torsion is Cohen-Lenstra distributed in the limit.

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