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

Large deviations of the interference in the Ginibre network model