probability-statistics / Discrepancy theory
For every zonotope $Z \subset \mathbb{R}^d$ and vectors $v_1,\ldots,v_n \in Z$, there are signs with $\sum_i x_i v_i \in C\sqrt{d}\,Z$ for a universal constant $C$. This resolves a 2002 conjecture on vector balancing in zonotopes.
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For every zonotope $Z \subset \mathbb{R}^d$ and vectors $v_1,\ldots,v_n \in Z$, there are signs with $\sum_i x_i v_i \in C\sqrt{d}\,Z$ for a universal constant $C$. This resolves a 2002 conjecture on vector balancing in zonotopes.
Research memory
For every zonotope $Z \subset \mathbb{R}^d$ and vectors $v_1,\ldots,v_n \in Z$, there are signs with $\sum_i x_i v_i \in C\sqrt{d}\,Z$ for a universal constant $C$. This resolves a 2002 conjecture on vector balancing in zonotopes.
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