Small Ball Estimates for Quasi-Norms

Omer Friedland (), Ohad Giladi () and Olivier Guédon ()
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Omer Friedland: Université Pierre et Marie Curie
Ohad Giladi: University of Newcastle
Olivier Guédon: Université Paris-Est

Journal of Theoretical Probability, 2016, vol. 29, issue 4, 1624-1643

Abstract: 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 results which were previously obtained in Friedland and Sodin (C R Math Acad Sci Paris 345(9):513–518, 2007), and Rudelson and Vershynin (Commun Pure Appl Math 62(12):1707–1739, 2009).

Keywords: Small ball estimates; Sobolev norm; Littlewood–Offord type estimates; 60D05 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10959-015-0622-z

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