Abstract
Given 0<s<\frac{d}{2} with s\leq 1 , we are interested in the large N -behavior of the optimal constant \kappa_{N} in the Hardy inequality \sum_{n=1}^{N} (-\Delta_{n})^{s} \geq \kappa_{N} \sum_{n<m}|X_{n}-X_{m}|^{-2s} , when restricted to antisymmetric functions. We show that N^{1-\frac{2s}{d}}\kappa_{N} has a positive, finite limit given by a certain variational problem, thereby generalizing a result of Lieb and Yau related to the Chandrasekhar theory of gravitational collapse.
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