For weakly time-stationary spatio-temporal point processes with sub-quadratic variance growth, the empirical Kantorovich-Rubinstein distance converges at rates matching classical Wasserstein rates in intrinsic dimension, up to logarithms.
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Sharp Convergence Rates of Empirical Unbalanced Optimal Transport for Spatio-Temporal Point Processes
For weakly time-stationary spatio-temporal point processes with sub-quadratic variance growth, the empirical Kantorovich-Rubinstein distance converges at rates matching classical Wasserstein rates in intrinsic dimension, up to logarithms.