Dimensionality reduction on vector spaces using complex random matrices

In this thesis we present part of a wider work regarding dimensionality reduction on the Euclidean space. Specifically we focus on finding concentration bounds for sums of Rademacher Chaoses. We will see why these bounds are useful in dimensionality reduction and we'll show the mathematical theory needed to obtain them. Finally we will provide a formal derivation of a concentration bound that directly follows from the theory.