Bergman kernel asymptotics for singular metrics on punctured Riemann   surfaces
  We consider singular metrics on a punctured Riemann surface and on a line bundle and study the behavior of the Bergman kernel in the neighbourhood of the punctures. The results have an interpretation in terms of the asymptotic profile of the density of states function of the lowest Landau level in quantum Hall effect. 
Dan Coman, Semyon Klevtsov, George Marinescu
math.CV cond-mat.str-el hep-th math-ph math.MP