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Vector Balancing in Lebesgue Spaces Reis, Victor
Description
The Komlós conjecture in discrepancy theory asks for a ±1-coloring, for any given unit vectors, achieving constant discrepancy in the ell-infinity norm. We investigate what ell-q discrepancy bound to expect, more generally, for ±1-colorings of vectors in the unit ell-p ball for any p less than q, and achieve optimal partial colorings. In particular, for p = q, our result generalizes Spencer's "six standard deviations" theorem.
Item Metadata
| Title |
Vector Balancing in Lebesgue Spaces
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| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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| Date Issued |
2020-10-02T08:45
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| Description |
The Komlós conjecture in discrepancy theory asks for a ±1-coloring, for any given unit vectors, achieving constant discrepancy in the ell-infinity norm. We investigate what ell-q discrepancy bound to expect, more generally, for ±1-colorings of vectors in the unit ell-p ball for any p less than q, and achieve optimal partial colorings. In particular, for p = q, our result generalizes Spencer's "six standard deviations" theorem.
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| Extent |
29.0 minutes
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| Subject | |
| Type | |
| File Format |
video/mp4
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| Language |
eng
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| Notes |
Author affiliation: University of Washington
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| Series | |
| Date Available |
2021-04-01
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0396452
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| URI | |
| Affiliation | |
| Peer Review Status |
Unreviewed
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| Scholarly Level |
Graduate
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| Rights URI | |
| Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International