On (ε,k)-min-wise independent permutations

We study the phase transition of the minimum degree multi-graph process. We prove that for a constant hg ≈ 0.8607, with probability tending to 1 as n → ∞, the graph consists of small components on O(log n) vertices when the number of edges of a graph generated so far is smaller than hgn, the largest component has order roughly n when the number of edges added is exactly hgn, and the graph consists of one giant component on Θ(n) vertices and small components on O(log n) vertices when the number of edges added is larger than hgn.