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Anomalous centrality evolution of two-particle angular correlations observedin Au-Au collisions at $\sqrt{s_{NN}} = 62$ and 200 GeV and the onset of ridgestructures are considered in the model of interacting quark-gluon strings. Weassume that at the given energy of nucleus-nucleus collisions the criticalenergy density may be reached at the specific centrality. In a stringpercolation model this might be treated equivalently to a formation of a largecluster of strings characterized by the critical string density, with a sizecomparable to the whole area of interaction of two nuclei. This hypothesisallows to define some constraints on the string percolation model using data ontransitional centralities in Au-Au collisions at these two energies. Resultsare extrapolated to the LHC energy where high string densities (exceeding thecritical value) are confirmed for all classes of centralities in Pb-Pbcollisions.  Interaction between strings inside large clusters formed in nucleus-nucleuscollisions is considered in a simplified Monte Carlo model. This model isapplied to the qualitative analysis of the onset of collectivity and the ridgeformation in Pb-Pb collisions. It is shown that the approach of the repulsivestring-string interaction is capable to explain the appearance of elliptic andtriangular flow observed in nucleus-nucleus collisions at RHIC and LHCenergies.

Constraints on string percolation model from anomalous centrality evolution data in Au-Au collisions at $\mathbf{\sqrt{s_{NN}}=}$ 62 and 200 GeV