Concentration dimension
In mathematics — specifically, in probability theory — the concentration dimension of a Banach space-valued random variable is a numerical measure of how “spread out” the random variable is compared to the norm on the space.Definition
Let be a Banach space and let X be a Gaussian random variable taking values in B. That is, for every linear functional ℓ in the dual space B∗, the real-valued random variable ⟨ℓ, X⟩ has a normal distribution. Define
Then the concentration dimension d of X is defined byExamples
