  We obtain non asymptotic bounds for the Monte Carlo algorithm associated to
the Euler discretization of some diffusion processes. The key tool is the
Gaussian concentration satisfied by the density of the discretization scheme.
This Gaussian concentration is derived from a Gaussian upper bound of the
density of the scheme and a modification of the so-called "Herbst argument"
used to prove Logarithmic Sobolev inequalities. We eventually establish a
Gaussian lower bound for the density of the scheme that emphasizes the
concentration is sharp.
