LARGE N LIMIT IN THE QUANTUM HALL-EFFECT

The Laughlin states for N interacting electrons at the plateaus of the fractional Hall effect are studied in the thermodynamic limit of larg e N. It is shown that this limit leads to the semiclassical regime for these states, thereby relating their stability to their semiclassical nature. The equivalent problem of two-dimensional plasmas is solved a nalytically, to leading order for N-->infinity, by the saddle-point ap proximation - a two-dimensional extension of the method used in random matrix models of quantum gravity and gauge theories. To leading order , the Laughlin states describe classical droplets of fluids with unifo rm density and sharp boundaries, as expected from the Laughlin ''plasm a analogy''. In this limit, the dynamical W(infinity)-symmetry of the quantum Hall states expresses the kinematics of the area-preserving de formations of incompressible liquid droplets.