Norms of weighted sums of log-concave random vectors

2019/06/09 by Chasapis, Giorgos, Giannopoulos, Apostolos, Skarmogiannis, Nikos
#FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Probability (math.PR)

paper · doi:10.48550/arxiv.1906.03719

Abstract

Let C and K be centrally symmetric convex bodies of volume 1 in \mathbb Rⁿ. We provide upper bounds for the multi-integral expression ‖\bf t‖_C^s,K=∫_C⋯∫_C‖∑_j=1^st_jx_j‖_K dx₁⋯ dx_s in the case where C is isotropic. Our approach provides an alternative proof of the sharp lower bound, due to Gluskin and V. Milman, for this quantity. We also present some applications to "randomized" vector balancing problems.

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