  We study the formation and evolution of domain walls with initial
inflationary fluctuations by numerical lattice calculations that, for the first
time, correctly take into account correlations on superhorizon scales. We find
that, contrary to the widely-held claim {over the past few tens of years}, the
domain wall network exhibits remarkable stability even when the initial
distribution is largely biased toward one of the minima. This is due to the
fact that the domain wall network retains information about initial conditions
on superhorizon scales, and that the scaling solution is not a local attractor
in this sense. Our finding immediately implies that such domain walls will have
a significant impact on cosmology, including the production of gravitational
waves, baryogenesis, and dark matter from domain walls. Applying this result to
the axion-like particle domain wall, we show that it not only explains the
isotropic cosmic birefringence suggested by the recent analysis, but also
predicts anisotropic cosmic birefringence that is nearly scale-invariant on
large scales and can be probed by future CMB observations.
