This book had a previous edition [132]. The changes between the two editions are not only
cosmetic or pedagogical, and the degree of improvement in the mathematics themselves is …

What is the maximum level a certain river is likely to reach over the next 25 years?(Having
experienced three times a few feet of water in my house, I feel a keen personal interest in …

Majorizing measures provide bounds for the supremum of stochastic processes. They
represent the most general possible form of the chaining argument going back to …

A precise link proved by Kuelbs and Li relates the small ball behavior of a Gaussian
measure $\mu $ on a Banach space $ E $ with the metric entropy behavior of $ K_\mu $, the …

This survey addresses sampling discretization and its connections with other areas of
mathematics. The survey concentrates on sampling discretization of norms of elements of …

Let Φ∈ Rm xn be a sparse Johnson-Lindenstrauss transform [52] with column sparsity s.
For a subset T of the unit sphere and ε∈(0, 1/2), we study settings for m, s to ensure EΦ …

1. Introduction. Consider a random variable (rv) h such that Eh2< 0, and consider an
independent, identically distributed (iid) sequence (hk) k> l distributed like h. To each t=(tk) …

We present algorithmic applications of an approximate version of Caratheodory's theorem.
The theorem states that given a set of vectors X in Rd, for every vector in the convex hull of X …

This text considers a specific Volterra integral operator and investigates its degree of
compactness in terms of properties of certain kernel functions. In particular, under certain …

The approximate Carathéodory theorem states that given a compact convex set C ⊂ R^ n
C⊂ R n and p ∈ 2,+ ∞ p∈ 2,+∞, each point x^* ∈ C x∗∈ C can be approximated to ϵ ϵ …