Diffusion Approximation for the Components in Critical Inhomogeneous Random Graphs of Rank 1.
Consider the random graph on n vertices 1,...,n. Each vertex i is assigned a type x(i) with x(1),...,x(n) being independent identically distributed as a nonnegative random variable X. We assume that EX3 < infinity. Given types of all vertices, an edge exists between vertices i and j independent of anything else and with probability min{1, x(i)x(j)/n (1 + a/n(1/3))}. We study the critical phase, wh