Exponential decay of correlations in the one-dimensional Coulomb gas ensembles
We consider the Gibbs measure on the configurations of N particles on R+ with one fixed particle at one end at 0. The potential includes pair-wise Coulomb interactions between any particle and its 2K neighbors. Only when K = 1, the model is within the rank-one operators, and it was treated previously. Here, for the case K ≥ 2, exponentially fast convergence of density distribution for the spacings