  We consider the median of n independent Brownian motions, and show that this
process, when properly scaled, converges weakly to a centered Gaussian process.
The chief difficulty is establishing tightness, which is proved through direct
estimates on the increments of the median process. An explicit formula is given
for the covariance function of the limit process. The limit process is also
shown to be Holder continuous with exponent gamma for all gamma < 1/4.
