The covering number of the standard simplex is the minimal number of $k$-dimensional balls of radius $\epsilon$ that suffices for covering the probability simplex $\{x \in \mathbb{R}^{k} : x_1 + \dots + x_k = 1, x_i \ge 0, i=1, \dots, k \}$.
A simple argument shows that this cover number is asymptotically $\Theta(\epsilon^{1-k})$. Is there a standard reference for this claim?
