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On the reduction of a random basis

Ali AkhaviJean-François MarckertAlain Rouault — 2009

ESAIM: Probability and Statistics

For , let be independent random vectors in n with the same distribution invariant by rotation and without mass at the origin. Almost surely these vectors form a basis for the Euclidean lattice they generate. The topic of this paper is the property of reduction of this random basis in the sense of Lenstra-Lenstra-Lovász (LLL). If b ^ 1 ( n ) , ... , b ^ p ( n ) is the basis obtained from by Gram-Schmidt orthogonalization, the quality of the reduction depends upon the sequence of ratios of squared lengths of consecutive vectors...

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