Moments of the Distance Between Independent Random Vectors
summary
Proves quantitative reversals of the triangle-integral bound for independent Banach-space-valued vectors and identifies optimal constants: constant 3 for p=1 and generally about 2(3/2)^p for p>1, with matching counterexamples built by embedding a complete bipartite graph metric into l∞ and slicing onto a hyperplane. Main tools are complex interpolation and spectral methods* plus nonlinear isometric embeddings; gives exact j_p for L_q, partial roundness results, and several open problems about weakening independence.
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