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We study the asymptotic distribution of the number of matchings of size$\ell=\ell(n)$ in $G(n,p)$ for a wide range of $p=p(n)\in (0,1)$ and for every$1\le \ell\le \lfloor n/2\rfloor$. We prove that this distribution changes fromnormal to log-normal as $\ell$ increases, and we determine the critical valueof $\ell$, as a function of $n$ and $p$, at which the transition of thelimiting distribution occurs.

A transition of limiting distributions of large matchings in random graphs