Uniform random complex top-homology asymptotic conjecture

Let $\mathbb{F}$ be a field and let $\Delta\tooltip\sim \mathcal{U}(n)$, where $n$ is even. Here $\mathcal{U}(n)$ denotes the uniform random simplicial complex on $[n]$. Top-homology asymptotic conjecture. With high probability,

$$\dim H_{n/2-1}(\Delta,\mathbb{F})=(1+o(1))\frac{2^{(n-1)/2}}{\sqrt{\pi n}}.$$

This is presented as an essentially best-possible refinement of the preceding theorem on the top homology of uniform random complexes; its resolution is not given in the source.