Covering numbers of Gaussian reproducing kernel Hilbert spaces

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Variance-based Regularization with Convex Objectives (2016, background): “) To illustriate this point, we consider the case where F is a bounded subset of a reproducing kernel Hilbert space generated by some sufficiently nice kernel K; even for the Gaussian kernel K(x, z) = exp(−(1) 2 ‖x− z‖ (2)), log covering numbers for such function spaces grow at least exponentially i”
Minimax Statistical Learning and Domain Adaptation with Wasserstein Distances (2017, background): “To that end, we need the following estimate due to Cucker and Zhou [13, Thm 5.1] (which was later shown by Kühn [14] to be asymptotically exact up to the double logarithmic factor): Proposition 3.2.”