  We numerically examine the effect of thermal fluctuations on a first-order
phase transition in 2+1 dimensions. By focusing on the expansion of a single
bubble we are able to calculate changes in the bubble wall's velocity as well
as changes in its structure relative to the standard case where the bubble
expands into a homogeneous background. Not only does the wall move faster, but
the transition from the symmetric to the asymmetric phase is no longer smooth,
even for a fairly strong transition. We discuss how these results affect the
standard picture of electroweak baryogenesis.
