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arXiv · 1410.0780

Small ball estimates for quasi-norms

Omer Friedland·Ohad Giladi·Olivier Guédon
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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 vectors under some smoothness assumptions on their density function. In the second part, we obtain Littlewood-Offord type estimates for quasi-norms. This generalizes a result which was previously obtained by Friedland and Sodin and by Rudelson and Vershynin.

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Omer Friedland, Ohad Giladi, Olivier Guédon. 2015-07-29. Small ball estimates for quasi-norms. https://doi.org/10.1007/s10959-015-0622-z

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