  In this note, we consider random walks in the quarter plane with arbitrary
big jumps. We announce the extension to that class of models of the analytic
approach of [G. Fayolle, R. Iasnogorodski, and V. Malyshev, Random walks in the
quarter plane, Springer-Verlag, Berlin (1999)], initially valid for walks with
small steps in the quarter plane. New technical challenges arise, most of them
being tackled in the framework of generalized boundary value problems on
compact Riemann surfaces.
