For every prime p, the dimension of H_1(T_n, F_p) of a random 2-dimensional determinantal hypertree and of a random 1-out 2-complex is o(n^2) in probability.
The large deviation principle for the Erdős- Rényi random graph.European Journal of Combinatorics, 32(7):1000–1017, 2011
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Using dense graph limit theory to count cocycles of random simplicial complexes
For every prime p, the dimension of H_1(T_n, F_p) of a random 2-dimensional determinantal hypertree and of a random 1-out 2-complex is o(n^2) in probability.