Inverse Littlewood-Offord problems for quasi-norms

Title: Inverse Littlewood-Offord problems for quasi-norms
Creator: Friedland, Omer; Giladi, Ohad; Guédon, Olivier
Relation: Discrete & Computational Geometry Vol. 57, Issue 1, p. 231-255
Publisher Link: http://dx.doi.org/10.1007/s00454-016-9829-8
Publisher: Springer
Resource Type: journal article
Date: 2017
Description: Given a compact star-shaped domain K⊆ℝ^d, n vectors v₁,…,v_n∈ℝ^d, a number R > 0, and i.i.d. random variables η₁,…,η_n, we study the geometric and arithmetic structure of the multi-set V = {v₁,…,v_n} under the assumption that the concentration function [formula could not be replicated] does not decay too fast as n → ∞. This generalises the case where K is the Euclidean ball, which was previously studied in Nguyen and Vu (Adv Math 226(6):5298–5319, 2011) and Tao and Vu (Combinatorica 32(3):363–372, 2012), to the non-Euclidean settings, that is, to general norms and quasi-norms in ℝ^d.
Subject: concentration function; Quasi-norm; inverse Littlewood-Offord problems
Identifier: http://hdl.handle.net/1959.13/1397453
Identifier: uon:34275
Identifier: ISSN:0179-5376
Language: eng
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