Why are Gaussian valued random variables so important in the Geometry of Banach spaces? I am reading the monograph by Pisier - "Probabilistic Methods in the Geometry of Banach Spaces" and in the very first chapter - "Dvoretzky's theorem by Gaussian Methods" there are definitions using B valued gaussian random variables X (where B is the Banach space under consideration).

Intuitively, what is the reason that would make one look toward gaussian variables - as opposed to Bernoulli rv (which I guess are also used in several definitions).