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Norms of weighted sums of log-concave random vectors

    https://doi.org/10.1142/S0219199719500366Cited by:1 (Source: Crossref)

    Let CC and KK be centrally symmetric convex bodies of volume 1 in n. We provide upper bounds for the multi-integral expression

    tCs,K=CCsj=1tjxjKdx1dxs
    in the case where C is isotropic. Our approach provides an alternative proof of the sharp lower bound, due to Gluskin and Milman, for this quantity. We also present some applications to “randomized” vector balancing problems.

    AMSC: 52A23, 46B06, 52A40, 60D05
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