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We develop a new technique for establishing quantitative propagation of chaosfor systems of interacting particles. Using this technique we prove propagationof chaos for diffusing particles whose interaction kernel is merely H\"oldercontinuous, even at long ranges. Moreover, we do not require specially preparedinitial data. On the way, we establish a law of large numbers for SDEs thatholds over a class of vector fields simultaneously. The proofs bring togetherideas from empirical process theory and stochastic flows.

Propagation of chaos for H\"older continuous interaction kernels via Glivenko-Cantelli