A Central Limit Theorem and Exponential Correlation Decay for the Coulomb Chain

We study the Coulomb chain where particles are restricted to one dimension and experience three-dimensional Coulomb interactions with their nearest and next-to-nearest neighbours. The distances between consecutive particles are treated as random variables. It is shown that the correlation between clusters of consecutive variables decay exponentially with the number of variables separating them. This result is then used to prove a central limit theorem.