A probabilistic result for the max-cut problem on random graphs

We consider the max-cut problem on a random graph G with n vertices and weights wij being independent bounded random variables with the same fixed positive expectation μ and variance σ ². It is well known that the max-cut number mc(G) always exceeds ½ Σi<j wij. We prove that with probability greater than pn the max-cut number satisfies ½ Σi<j wij ⩽ mc(G) ⩽ qn (½ Σi<j wij), where pn,qn are explicitly erxpressed in terms of the problem's data and such that pn,qn approach 1 as n → ∞.