2015/06/01 by Christian Hirsch, Hirsch, Christian, Benedikt Jahnel +5
Decision Sciences · Mathematics · #Probability and Risk Models #Stochastic processes and statistical mechanics #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.1506.00576
We study large-deviation principles for a model of wireless networks\nconsisting of Poisson point processes of transmitters and receivers,\nrespectively. To each transmitter we associate a family of connectable\nreceivers whose signal-to-interference-and-noise ratio is larger than a certain\nconnectivity threshold. First, we show a large-deviation principle for the\nempirical measure of connectable receivers associated with transmitters in\nlarge boxes. Second, making use of the observation that the receivers\nconnectable to the origin form a Cox point process, we derive a large-deviation\nprinciple for the rescaled process of these receivers as the connection\nthreshold tends to zero. Finally, we show how these results can be used to\ndevelop importance-sampling algorithms that substantially reduce the variance\nfor the estimation of probabilities of certain rare events such as users being\nunable to connect\n