  A Brownian motion model is devised on the manifold of S-matrices, and applied
to the calculation of conductance-conductance correlations and of the weak
localization peak. The model predicts that (i) the correlation function in $B$
has the same shape and width as the weak localization peak; (ii) the functions
behave as $\propto 1-{\cal O}(B^2)$, thus excluding a linear line shape; and
(iii) their width increases as the square root of the number of channels in the
leads. Some of these predictions agree with experiment and with other
calculations only in the limit of small $B$ and a large number of channels.
