- 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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