Random Magnetic Impurities and the $\delta$ Impurity Problem
  One considers the effect of disorder on the 2-dimensional density of states of an electron in a constant magnetic field superposed onto a Poissonnian random distribution of point vortices. If one restricts the electron Hilbert space to the lowest Landau level of the total average magnetic field, the random magnetic impurity problem is mapped onto a contact $\delta$ impurity problem. A brownian motion analysis of the model, based on brownian probability distributions for arithmetic area winding sectors, is also proposed. PACS numbers: 05.30.-d, 05.40.+j, 11.10.- 
Jean DESBOIS, Cyril FURTLEHNER and St\'ephane OUVRY, Division de   Physique Th\'eorique, IPN, Orsay Fr-91406