BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Vector Balancing in Lebesgue Spaces Reis, Victor


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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