LEVY STABLE LAW DESCRIPTION OF INTERMITTENT BEHAVIOR AND QUARK GLUON PLASMA PHASE-TRANSITIONS

Levy stable laws are introduced to describe intermittency in multiparticle production, using a generalization of the central limit theorem applied to random cascading models. This gives a one-parameter family of representative models depending continuously on the Levy index mu. The multifractal spectrum, the associate "free energy" and the phase diagram of random cascading are retrieved. This helps classifying intermittency patterns due to different kind of phase transitions, either thermal mu < 1: quark-gluon plasma, or non-thermal mu > 1: cascading process. Bin-bin factorial correlations are shown to be very sensitive to the Levy index mu. We suggest to measure them in heavy-ion reactions as a clear signals of a quark-gluon plasma and its decay into hadrons.