Small ball estimates for quasi-norms
Probability
2015-07-30 v3
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.
Keywords
Cite
@article{arxiv.1410.0780,
title = {Small ball estimates for quasi-norms},
author = {Omer Friedland and Ohad Giladi and Olivier Guédon},
journal= {arXiv preprint arXiv:1410.0780},
year = {2015}
}
Comments
Minor corrections. To appear in J Theor Probab