Hypercontractivity and Lower Deviation Estimates in Normed Spaces

Grigoris Paouris, Konstantin Tikhomirov, Petros Valettas

We consider the problem of estimating small ball probabilities $\mathbb{P}\{f(G)⩽\delta \mathbb{E}f(G)\}$ for sub-additive,positively homogeneous functions $f$ with respect to th…