  We show that there exists a strong connection between the generic formal
neighborhood at a rational arc lying in the Nash set associated with a toric
divisorial valuation on a toric variety and the formal neighborhood at the
generic point of the same Nash set. This may be interpreted as the fact that,
analytically along such a Nash set, the arc scheme of a toric variety is a
product of a finite dimensional singularity and an infinite dimensional affine
space.
