The conductance distribution of metallic mesoscopic systems is considered.
The variance of this distribution describes the universal conductance
fluctuations, yielding a Gaussian distribution of the conductance. We calculate
diagrammatically the third cumulant of this distribution, the leading deviation
from the Gaussian. We confirm random matrix theory calculations that the
leading contribution in quasi-one dimension vanishes. However, in quasi two
dimensions the third cumulant is negative, whereas in three dimensions it is
positive.Comment: 9 pages, Revtex, with eps figures,to appear in Phys Rev