Asymptotics of k-nearest Neighbor Riesz Energies

We obtain new asymptotic results about systems of N particles governed by Riesz interactions involving k-nearest neighbors each particle as $$N\rightarrow \infty $$ . These include a generalization to weighted potentials with external field. Such offer an appealing alternative other approaches for reducing the computational complexity N-body interaction. find first-order term large asymptotics and characterize limiting distribution minimizers. also \Gamma -convergence such interactions, describe minimizers on 1-dimensional flat torus in absence field, all N.