  It is known that a light scalar field obtains fluctuations in the de Sitter
inflationary background. Such fluctuations could provide an initial condition
for baryogenesis through the Affleck-Dine mechanism, where an approximate
$U(1)_B$ symmetry is usually assumed. However, an interpretation of the baryon
number generation in this way is strongly related to the correlation length of
the angular mode. In this work, we calculate the correlation length of the
angular mode for a model exhibiting an approximate $U(1)$ symmetry. We find
that for a massive nearly non-interacting field, the correlation length of the
angular mode is determined by the mass parameter of the model and it is similar
to $H^{-1} \exp(H^2/m^2)$. Applying this result to baryogenesis via the
Affleck-Dine mechanism with a stochastic origin, we find that only for $m \ll
\mathcal O(0.1) H$(assuming $N_*=60$) can the correlation length of the baryon
number density be much larger than our current horizon size, such that we live
in the baryon-rich region. If this is not true, in the early time our universe
would consist of numerous patches of baryon-rich and anti-baryon-rich regions
with the average baryon number being nearly zero.
