Statistical correlations in a Coulomb gas with a test charge

A recent paper [Jokela et al., arxiv:0806.1491 (2008)] contains a surmise about an expectation value in a Coulomb gas which interacts with an additional charge ξ that sits at a fixed position. Here I demonstrate the validity of the surmised expression and extend it to a certain class of higher cumulants. The calculation is based on the analogy to statistical averages in the circular unitary ensemble of random-matrix theory and exploits properties of orthogonal polynomials on the unit circle. PACS numbers: 02.50.Sk, 05.20.-y, 05.30.Fk, 05.45.Mt 1. Purpose and result In a recent paper Jokela, Järvinen and Keski-Vakkuri studied n-point functions in timelike boundary Liouville theory via the analogy to a Coulomb gas on a unit circle [1]. In this analogy, N unit charges at position ti interact with additional charges of integer value ξa, situated at position τa. To illustrate this technique the authors of [1] considered the canonical expectation value 〈·〉 ≡ 1 Z ∫ N ∏