Energy of the Coulomb gas on the sphere at low temperature

Abstract

We consider the Coulomb gas of $N$ particles on the sphere and show that the logarithmic energy of the configurations approaches the minimal energy up to an error of order $\log N$, with exponentially high probability and on average, provided the temperature is $\mathcal{O}(1/N)$.

11 pages; revised argument in the proof of Proposition 3.1, results unchanged