Abstract
We develop a technique for computing expected numbers of
vacua in gaussian ensembles of supergravity theories, and apply it
to derive an asymptotic formula for the index counting all flux
supersymmetric vacua with signs in Calabi-Yau compactification of
type 
b string theory, which becomes exact in the limit
of a large number of fluxes. This should give a reasonable estimate
for actual numbers of vacua in string theory, for CY's with small
b3.
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