  In this paper we give a new proof of the universality of the Tutte polynomial
for matroids. This proof uses appropriate characters of Hopf algebra of
matroids, algebra introduced by Schmitt (1994). We show that these Hopf algebra
characters are solutions of some differential equations which are of the same
type as the differential equations used to describe the renormalization group
flow in quantum field theory. This approach allows us to also prove, in a
different way, a matroid Tutte polynomial convolution formula published by
Kook, Reiner and Stanton (1999). This FPSAC contribution is an extended
abstract.
