A transition of limiting distributions of large matchings in random graphs
Gao, Pu · Sato, Cristiane M.
Original · EN
We study the asymptotic distribution of the number of matchings of size ℓ=ℓ(n) in G(n,p) for a wide range of p=p(n)∈ (0,1) and for every 1≤ ℓ≤ n/2. We prove that this distribution changes from normal to log-normal as ℓ increases, and we determine the critical value of ℓ, as a function of n and p, at which the transition of the limiting distribution occurs.
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