Entropy of convex hulls and the probability of small balls

The problem of estimating entropy numbers of convex hulls has attracted researchers in geometrical functional analysis over the last 30 years. At first, we tend to shed some light on the tight relations between linear operators, Gaussian stochastic processes and convex hulls. In a second step, we will show how to treat the analytical task to estimate the entropy numbers of convex hulls in Hilbert space using a probabilistic approach. In particular, a precise link between the convex hull and the reproducing kernel Hilbert space of a Gaussian process enables us to employ results on small ball probabilities. Vice versa, we show how small ball probability estimates can be obtained from the entropy of convex hulls.