  Under different assumptions on the distribution of the fading random
variables, we derive large deviation estimates for the tail of the interference
in a wireless network model whose nodes are placed, over a bounded region of
the plane, according to the $\beta$-Ginibre process, $0<\beta\leq 1$. The
family of $\beta$-Ginibre processes is formed by determinantal point processes,
with different degree of repulsiveness, which converge in law to a homogeneous
Poisson process, as $\beta \to 0$. In this sense the Poisson network model may
be considered as the limiting uncorrelated case of the $\beta$-Ginibre network
model. Our results indicate the existence of two different regimes. When the
fading random variables are bounded or Weibull superexponential, large values
of the interference are typically originated by the sum of several equivalent
interfering contributions due to nodes in the vicinity of the receiver.
  In this case, the tail of the interference has, on the log-scale, the same
asymptotic behavior for any value of $0<\beta\le 1$, but it differs (again on a
log-scale) from the asymptotic behavior of the tail of the interference in the
Poisson network model.
  When the fading random variables are exponential or subexponential, instead,
large values of the interference are typically originated by a single
dominating interferer node and, on the log-scale, the asymptotic behavior of
the tail of the interference is essentially insensitive to the distribution of
the nodes. As a consequence, on the log-scale, the asymptotic behavior of the
tail of the interference in any $\beta$-Ginibre network model, $0<\beta\le 1$,
is the same as in the Poisson network model.
