Betti numbers of the moduli space of rational curves with n marked points and the Fulton-MacPherson configuration space are asymptotically normally distributed.
G¨ ottsche.The Betti numbers of the Hilbert scheme of ponts on a smooth projective surface
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Asymptotic distribution of the Betti numbers of $\overline{\mathcal{M}}_{0,n}$
Betti numbers of the moduli space of rational curves with n marked points and the Fulton-MacPherson configuration space are asymptotically normally distributed.