# Balancing Gaussian vectors in high dimension

@article{Meka2020BalancingGV, title={Balancing Gaussian vectors in high dimension}, author={Raghu Meka and Philippe Rigollet and Paxton Turner}, journal={ArXiv}, year={2020}, volume={abs/1910.13972} }

Motivated by problems in controlled experiments, we study the discrepancy of random matrices with continuous entries where the number of columns $n$ is much larger than the number of rows $m$. Our first result shows that if $\omega(1) \leq m \leq o(n)$, a matrix with i.i.d. standard Gaussian entries has discrepancy $\Theta(\sqrt{n} \, 2^{-n/m})$ with high probability. This provides sharp guarantees for Gaussian discrepancy in a regime that had not been considered before in the existing… CONTINUE READING

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