Distribution of point charges with small discrete energy

Pritsker, Igor

doi:10.1090/S0002-9939-2011-11135-3

Distribution of point charges with small discrete energy
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by Igor E. Pritsker PDF

Proc. Amer. Math. Soc. 139 (2011), 3461-3473 Request permission

Abstract:

We study the asymptotic equidistribution of points near arbitrary compact sets of positive capacity in $\mathbb {R}^d,\ d\ge 2$. Our main tools are the energy estimates for Riesz potentials. We also consider the quantitative aspects of this equidistribution in the classical Newtonian case. In particular, we quantify the weak convergence of discrete measures to the equilibrium measure and give the estimates of convergence rates for discrete potentials to the equilibrium potential.

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