Small ball estimates for quasi-norms

Title: Small ball estimates for quasi-norms
Creator: Friedland, Omer; Giladi, Ohad; Guédon, Olivier
Relation: Journal of Theoretical Probability Vol. 29, Issue 4, p. 1624-1643
Publisher Link: http://dx.doi.org/10.1007/s10959-015-0622-z
Publisher: Springer
Resource Type: journal article
Date: 2016
Description: 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).
Subject: small ball estimates; Sobolev norm; Littlewood–Offord type estimates
Identifier: http://hdl.handle.net/1959.13/1340196
Identifier: uon:28414
Identifier: ISSN:0894-9840
Language: eng
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