Some recent papers related to metric entropy

A Characterization of random Bloch functions. A necessary and sufficient condition is obtained for a random power series to be a Bloch function almost surely. The main tool is a large deviation inequality of Gaussian processes. (J. Math. Anal. App. 2000)

Metric entropy of convex hulls. It may take as many as $e^{cn^2(\log n)^2}$ balls of radius 1 to cover its covex hull, if it take $e^{n^2}$ balls of radius 1 to cover a set. (Israel J. Math 2001)

Majorizing measure bounds for Gaussian processes with exponential tails (Preprint)

Maximal operators and Hilbert transforms along convex curves. A necessary condition for the Maximal operator on a curve to be bounded in $L^p$.

Entropy of convex hulls in Hilbert spaces. A very sharp upper bound for the entropy of the absolute convex hull, given the entropy rate of the set of extreme points. (Bull. London Math. Soc 2004)

Non-zero boundaries of Leibniz half-space. For three or higher dimensional convex Banach space, the boundary of a Leibniz half space may have positive Lebesgue measure, solving a related conjecture. (Proc. Amer. Math. Soc. 2004)

Small ball probabilities for the Slepian Gaussian fields. (Abstract) (with W. Li) A Fourier analytic method handeling small deviation of Gaussian fields. (Trans. Amer. Math. Soc. 2006)

Metric entropy of high dimensional distributions and small ball probability of Brownian sheets. (abstract) (with R. Blei and W. Li) Bounds for the metric entropy of high dimensional distribution are obtained.

Metric entropy of monotonic functions (with J. Wellner) (Submitted to J. of Multivariate Anal.)