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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Submitted on : Tuesday, January 26, 2016 - 10:13:25 PM
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Omer Friedland, Ohad Giladi, Olivier Guédon. Small Ball Estimates for Quasi-Norms. Journal of Theoretical Probability, Springer, 2016, 29 (4), pp.1025-1049. ⟨10.1007/s10959-015-0622-z⟩. ⟨hal-01262620⟩

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