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Long range correlations multiplicity-multiplicity, $p_T^2$-multiplicity and$p^2 - p^2_T$ are studied in the percolating colour string picture underdifferent assumptions of the dynamics of string interaction. It is found thatthe strength of these correlations is rather insensitive to these assumptionsnor to the geometry of formed fused string clusters. Bothmultiplicity-multiplicity and $p_T^2$-multiplicity correlations are found toscale and depend only on the string density.  The $p_T^2$-multiplicity correlations, which are absent in the independentstring picture, are found to be of the order of 10% for central heavy ioncollisions and can serve as a clear signature of string fusion. In contrast the$p^2_T - p^2_T$ correlations turned out to be inversely proportional to thenumber of strings and so very small for relaistic collisions.Comment: 23 pages, 6 figure

Correlations between multiplicities and average transverse momentum in the percolating color strings approach