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Functional Central Limit Theorem for the Giant of Rank-One Random Graphs
The size of the largest connected component of a supercritical random graph, tracked as the connection parameter grows, fluctuates around its deterministic limit like a centered Gaussian process. This concept extends that process-level (functional) central limit theorem from the Erdos-Renyi graph to rank-one inhomogeneous models whose vertex-weight distribution converges together with its second moment, using a breadth-first-walk encoding.