  The large N limit has been successfully applied to QCD, leading to
qualitatively correct results even for N=3. In this work, we propose to treat
the number N=3 of Standard Model generations as a large number. Specifically,
we apply this idea to the neutrino anarchy scenario and study neutrino physics
using Random Matrix Theory, finding new results in both areas. For neutrino
physics, we obtain predictions for the masses and mixing angles as a function
of the generation number N. The Seesaw mechanism produces a hierarchy of order
1/N^3 between the lightest and heaviest neutrino, and a theta(13) mixing angle
of order 1/N, in parametric agreement with experimental data when N goes to 3.
For Random Matrix Theory, this motivates the introduction of a new type of
ensemble of random matrices, the "Seesaw ensemble." Basic properties of such
matrices are studied, including the eigenvalue density and the interpretation
as a Coulomb gas system. Besides its mathematical interest, the Seesaw ensemble
may be useful in random systems where two hierarchical scales exist.
