On potential and field fluctuations in classical charged systems

Using electrostatic identities the potential and microfield in a plasma, important for determining line shapes, are expressed as limits of local quantities. These are shown to be well defined for typical configurations of macroscopic, i.e., infinite systems (under some mild clustering assumptions). Their covariance contains a slowly decaying part (|x|^-1, for the potential) whose coefficient is universal whenever the Stillinger-Lovett second moment condition holds. We show further that the contributions from distant regions (which are equal to suitable averages over local regions) have a Gaussian distribution.