Event-by-event fluctuations in hydrodynamical description of heavy-ion collisions

Effects caused by the event-by-event fluctuation of the initial conditions in hydrodynamical description of high-energy heavy-ion collisions are investigated. Non-negligible effects appear for several observable quantities, even for a fixed impact parameter $\vec b $. They are sensitive to the equation of state, being the dispersions of the observable quantities in general smaller when the QGP phase appears at the beginning of hydrodynamic evolution than when the fluid remains hadron gas during whole the evolution.