  The large N limit of the hermitian matrix model in three and four Euclidean
space-time dimensions is studied with the help of the approximate
Renormalization Group recursion formula. The planar graphs contributing to wave
function, mass and coupling constant renormalization are identified and summed
in this approximation. In four dimensions the model fails to have an
interacting continuum limit, but in three dimensions there is a non trivial
fixed point for the approximate RG relations. The critical exponents of the
three dimensional model at this fixed point are $\nu = 0.665069$ and
$\eta=0.19882$. The existence (or non existence) of the fixed point and the
critical exponents display a fairly high degree of universality since they do
not seem to depend on the specific (non universal) assumptions made in the
approximation.
