On Laughlin's wave function for the fractional quantum Hall effect

Two-dimensional electron gases subjected to a perpendicular magnetic field display a curious physical effect known as the quantum Hall effect. In order to explain this effect, Laughlin proposed a simple wave function as an approximate ground state. Laughlin's function involves the power of a Vandermonde determinant and a Gaussian weight. This talk presents exact results on the L^2 norm and correlation functions in the limit of infinitely many particles when Laughlin's function is adapted to a cylindrical geometry. The results are also of interest for the classical statistical mechanics of Coulomb gases. The talk is based on joint work with Ruedi Seiler and Elliott H. Lieb.