Small ball estimates for quasi-norms
arXiv:1410.0780 · doi:10.1007/s10959-015-0622-z
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.
Minor corrections. To appear in J Theor Probab