Uniform Partition-Function Estimates for Coulomb Modulated Energy at All Positive Temperatures
We prove uniform-in-$N$ partition-function estimates at all positive temperatures for the centered modulated energy of logarithmic, Riesz, and Bessel--Riesz kernels on $\mathbb R^d$ in the locally square-integrable range $0\le s<d/2$. They yield finite-particle exponential integrability, quadratic behavior at small par...