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- W2604830358 abstract "We prove that the uniform probability measure μ on every ( n − k ) -dimensional projection of the n -dimensional unit cube verifies the variance conjecture with an absolute constant C Var μ | x | 2 ≤ C sup θ ∈ S n − 1 E μ 〈 x , θ 〉 2 E μ | x | 2 , provided that 1 ≤ k ≤ n . We also prove that if 1 ≤ k ≤ n 2 3 ( log n ) − 1 3 , the conjecture is true for the family of uniform probabilities on its projections on random ( n − k ) -dimensional subspaces." @default.
- W2604830358 created "2017-04-14" @default.
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- W2604830358 date "2017-11-01" @default.
- W2604830358 modified "2023-10-17" @default.
- W2604830358 title "The variance conjecture on projections of the cube" @default.
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- W2604830358 doi "https://doi.org/10.1016/j.jmaa.2017.05.071" @default.
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