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Large deviations of the interference in the Ginibre network model

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 $β$-Ginibre process, $0<β\leq 1$. The family of $β$-Ginibre processes is formed by determinantal point processes, with different degree of repulsiveness, which converge in law to a homogeneous Poisson process, as $β\to 0$. In this sense the Poisson network model may be considered as the limiting uncorrelated case of the $β$-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 $0<β\le 1$, 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 $β$-Ginibre network model, $0<β\le 1$, is the same as in the Poisson network model.