  In this paper we consider the distribution of the zeros of a real random
Bargmann-Fock function of one or more variables. For these random functions we
prove estimates for two types of families of events, both of which are large
deviations from the mean. First, we prove that the probability there are no
zeros in $[-r,r]^m\subset\R^m$ decays at least exponentially in terms of $r^m$.
For this event we also prove a lower bound on the order of decay, which we do
not expect to be sharp. Secondly, we compute the order of decay for the
probability of families of events where the volume of the complex zero set is
either much larger or much smaller then expected.
