Abstract
Let x 1, ..., x n be independent normally distributed vectors on R d. We determine the distribution function of the minimum norm of the 2n vectors ±x 1 ± x 2 ... ± x n.
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References
I. Bárány and B. Doerr, Balanced partitions of vector sequences, Linear Algebra and its Applications 414 (2006), 464–469.
I. Bárány and V. S. Grinberg, On some combinatorial questions in finite dimensional spaces, Linear Algebra and its Applications 41 (1981), 1–9.
S. N. Bernstein, On a modification of Chebyshev’s inequality and on the deviation in Laplace’s formula, Sobranie sochineniy, Vol. 4, Izd. Nauke, Moscow, 1964. (in Russian)
P. Erdős, On a lemma of Littlewood and Offord, American Mathematical Society. Bulletin 51 (1945), 898–902.
J. Spencer, Balancing games, Journal of Combinatorial Theory. Series B. 23 (1977), 68–74.
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This research was supported by an NSF Graduate Research Fellowship and NSF grant DMS-0635607.
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Costello, K.P. Balancing Gaussian vectors. Isr. J. Math. 172, 145–156 (2009). https://doi.org/10.1007/s11856-009-0068-z
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DOI: https://doi.org/10.1007/s11856-009-0068-z