Affiliation:
1. Department of Geometry, Bolyai Institute University of Szeged Szeged Hungary
2. Alfréd Rényi Institute of Mathematics Budapest Hungary
3. Department of Mathematics University of Washington Seattle USA
Abstract
AbstractWe extend classical estimates for the vector balancing constant of equipped with the Euclidean and the maximum norms proved in the 1980s by showing that for and , given vector families with , one may select vectors with
for , and
for . These bounds are sharp and asymptotically sharp, respectively, for . The proofs combine linear algebraic and probabilistic methods with a Gaussian random walk argument.
Funder
Hungarian Scientific Research Fund
National Science Foundation