Extremes of spatial shot noise processes

Anup Biswas and François Baccelli studied the scaling limit of a class of shot-noise fields defined on an independently marked stationary Poisson point process and with a power law response function. Under appropriate conditions, they showed that the shot-noise field can be scaled suitably to have a non degenerate alpha-stable limit, as the intensity of the underlying point process goes to infinity. More precisely, finite dimensional distributions  converge and the finite dimensional distributions of the limiting random field have i.i.d. stable random components. This limit is hence called the alpha- stable white noise field. Analogous results are also obtained for the extremal shot-noise field which converges to a Fréchet white noise field.