• Corpus ID: 244773062

A note on spherical discrepancy

@inproceedings{Lonke2021ANO,
  title={A note on spherical discrepancy},
  author={Y. Lonke},
  year={2021}
}
  • Y. Lonke
  • Published 30 October 2021
  • Mathematics
A non-algorithmic, generalized version of a recent result, asserting that a natural relaxation of the Komlós conjecture from boolean discrepancy to spherical discrepancy is true, is proved by a very short argument using convex geometry. 

References

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The Komlos Conjecture Holds for Vector Colorings

TLDR
Here it is proved that if the columns of A are assigned unit real vectors rather than +/- 1 then the Komlos conjecture holds with K=1, which opens the way to proving tighter efficient (polynomial-time computable) upper bounds for the conjecture using semidefinite programming techniques.

Gaussian discrepancy: a probabilistic relaxation of vector balancing

Spherical Discrepancy Minimization and Algorithmic Lower Bounds for Covering the Sphere

TLDR
The algorithm is used to give the first non-trivial lower bounds for the problem of covering a hypersphere by hyperspherical caps of uniform volume at least $2^{-o(\sqrt{n})}$.

Six standard deviations suffice

Given n sets on n elements it is shown that there exists a two-coloring such that all sets have discrepancy at most Knl/2, K an absolute constant. This improves the basic probabilistic method with