Small Ball Estimates for Quasi-Norms
Abstract
This note contains two types of small ball estimates for random vectors in finite dimensional spaces equipped with a quasi-norm. In the first part, we obtain bounds for the small ball probability of random vactors under some smoothness assumptions on their density functions. In the second part, we obtain Littlewood-Offord type estimates for quasi-norms. This generalizes a result which was previously obtained in [FS07, RV09].
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