  The fundamental theory of nature may allow a large landscape of vacua. Even
if the theory contains a unified gauge symmetry, the 22 flavor parameters of
the Standard Model, including neutrino masses, may be largely determined by the
statistics of this landscape, and not by any symmetry. Then the measured values
of the flavor parameters do not lead to any fundamental symmetries, but are
statistical accidents; their precise values do not provide any insights into
the fundamental theory, rather the overall pattern of flavor reflects the
underlying landscape. We investigate whether random selection from the
statistics of a simple landscape can explain the broad patterns of quark,
charged lepton, and neutrino masses and mixings. We propose Gaussian landscapes
as simplified models of landscapes where Yukawa couplings result from overlap
integrals of zero-mode wavefunctions in higher-dimensional supersymmetric gauge
theories. In terms of just five free parameters, such landscapes can account
for all gross features of flavor, including: the hierarchy of quark and charged
lepton masses; small quark mixing angles, with 13 mixing less than 12 and 23
mixing; very light Majorana neutrino masses, with the solar to atmospheric
neutrino mass ratio consistent with data; distributions for leptonic 12 and 23
mixings that are peaked at large values, while the distribution for 13 mixing
is peaked at low values; and order unity CP violating phases in both the quark
and lepton sectors. While the statistical distributions for flavor parameters
are broad, the distributions are robust to changes in the geometry of the extra
dimensions. Constraining the distributions by loose cuts about observed values
leads to narrower distributions for neutrino measurements of 13 mixing, CP
violation, and neutrinoless double beta decay.
