Limit theorems in discrete stochastic geometry

This overview surveys two general methods for establishing limit theorems for functionals in discrete stochastic geometry. The functionals of interest are linear statistics with the general representation ∑x∈X ξ (x,X ), where X is locally finite and where the interactions of x with respect to X , given by ξ (x,X ), exhibit spatial dependence. We focus on subadditive methods and stabilization methods as a way to obtain weak laws of large numbers and central limit theorems for normalized and re-scaled versions of ∑i=1 ξ (Xi,{X j}j=1), where X j, j ≥ 1, are i.i.d. random variables. The general theory is applied to particular problems in Euclidean combinatorial optimization, convex hulls, random sequential packing, and dimension estimation.