Short- and long-range rapidity correlations in the model with a lattice in transverse plane

In the framework of the quark-gluon string model we consider the various fluctuation and correlation observables used in the analysis of the multiparticle production in hadronic interactions at high energy. We express these observables through the fundamental string characteristics and analyze their resulting properties: the dependence on the width of observation window(s), the range of the correlation in rapidity, the intensive or strongly intensive behavior. To take into account the influence of a string fusion processes on the string characteristics and on the behavior of the observables. we use the version of string model with a lattice (grid) in the impact parameter plane. In particular we show that the observable between multiplicities in two acceptance windows separated in rapidity, which is a strongly intensive in the case with independent identical strings, loses this property, when we take into account the string fusion and the formation of strings of a few different types takes place in a collision. (author)