  In this paper, we shall precise the asymptotic behaviour of Newton polygons
of $L$ functions associated to character sums, coming from some $n$ variable
Laurent polynomials. In order to do this, we use the free sum on convex
polytopes. This operation allows the determination of the limit of generic
Newton polygons for the sum $\Delta=\Delta_1\oplus \Delta_2$ when we know the
limit of generic Newton polygons for each factor. To our knowledge, these are
the first results concerning the asymptotic behaviour of Newton polygons for
multivariable polynomials.
