log-Coulomb Gases in the Projective Line of a $$p$$-Field
log-Coulomb Gases in the Projective Line of a $$p$$-Field
This article extends recent results on log-Coulomb gases in a $$p$$ -field $$K$$ (i.e., a nonarchimedean local field) to those in its projective line $$\mathbb{P}^1(K)$$ , where the latter is endowed with the $$PGL_2$$ -invariant Borel probability measure and spherical metric. Our first main result is an explicit combinatorial formula …