Date of Original Version
The final publication is available at Springer via http://dx.doi.org/10.1007/s10955-015-1215-z
Abstract or Description
We investigate which nonlocal-interaction energies have a ground state (global minimizer). We consider this question over the space of probability measures and establish a sharp condition for the existence of ground states. We show that this condition is closely related to the notion of stability (i.e. H-stability) of pairwise interaction potentials. Our approach uses the direct method of the calculus of variations.
Journal of Statistical Physics, 159, 4, 972-986.