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Title: On the discrepancy of random low degree set systems

Motivated by the celebrated Beck‐Fiala conjecture, we consider the random setting where there arenelements andmsets and each element lies intrandomly chosen sets. In this setting, Ezra and Lovett showed andiscrepancy bound whenn ≤ mand anO(1) bound whenn ≫ mt. In this paper, we give a tightbound for the entire range ofnandm, under a mild assumption that. The result is based on two steps. First, applying the partial coloring method to the case whenand using the properties of the random set system we show that the overall discrepancy incurred is at most. Second, we reduce the general case to that ofusing LP duality and a careful counting argument.

 
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NSF-PAR ID:
10161536
Author(s) / Creator(s):
 ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
Random Structures & Algorithms
Volume:
57
Issue:
3
ISSN:
1042-9832
Page Range / eLocation ID:
p. 695-705
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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