For at least 90% of an orthonormal basis of directions, linear functionals on uniform points in centered unit-volume convex bodies satisfy c sqrt(p) L2 <= Lp <= C sqrt(p) L2 with absolute c,C, for p up to n.
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Dimension-free Gaussian tail estimates for linear functionals on convex bodies
For at least 90% of an orthonormal basis of directions, linear functionals on uniform points in centered unit-volume convex bodies satisfy c sqrt(p) L2 <= Lp <= C sqrt(p) L2 with absolute c,C, for p up to n.