  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.-
