Event-by-event physics in relativistic heavy-ion collisions

Motivated by forthcoming experiments at RHIC and LHC, and results from SPS. a review is given of the present state of event-by-event fluctuations in u ltrarelativistic heavy-ion collisions. Fluctuations in particle multiplicit ies, ratios, transverse momenta, rapidity, etc. are calculated in participa nt nucleon as well as thermal models. The physical observables, including m ultiplicity, kaon-to-pion ratios, and transverse momenta agree well with re cent NA49 data at the SPS, and indicate that such studies do not yet reveal the presence of new physics. Predictions for RHIC and LHC energies are giv en. The centrality dependence with and without a phase transition to a quar k-gluon plasma is discussed - in particular, how the physical quantities ar e expected to display a qualitative different behavior in case of a phase t ransition, and can be signaled by anomalous fluctuations and correlations i n a number of observables. (C) 2001 Elsevier Science B.V. All rights reserv ed.