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We consider a system of particles on a finite interval with Coulomb3-dimensional interactions between close neighbours, i.e. only a few otherneighbours apart. This model was introduced by Malyshev [Probl. Inf. Transm. 51(2015) 31-36] to study the flow of charged particles. Notably even thenearest-neighbours interactions case, the only one studied previously, wasproved to exhibit multiple phase transitions depending on the strength of theexternal force when the number of particles goes to infinity.  Here we include as well interactions beyond the nearest-neighbours ones.Surprisingly but this leads to qualitatively new features even when theexternal force is zero. The order of the covariances of distances between pairsof consecutive charges is changed when compared with the formernearest-neighbours case, and moreover the covariances exhibit periodicity insign: the interspacings are positively correlated if the number ofinterspacings between them is odd, otherwise, they are negatively correlated.  In the course of the proof we derive Gaussian approximation for the limitdistribution for dependent variables described by a Gibbs distribution.

Covariance Structure of Coulomb Multiparticle System