A Central Limit Theorem For Incomplete U-Statistics Over Triangular Arrays

We analyze the fluctuations of incomplete U-statistics over a triangular array of independent random variables. We give criteria for a Central Limit Theorem (CLT, for short) to hold in the sense that we prove that an appropriately scaled and centered version of the U-statistic converges to a normal random variable. Our method of proof relies on a martingale CLT. An application, a CLT for the hitting time for random walks on random graphs, will be presented in Lowe and Terveer (2020).