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- W96374469 abstract "We survey two general methods for establishing limit theorems for functionals in discrete stochastic geometry. The functionals are linear statistics with the general representation $$sum _{xin mathcal{X}}xi (x,mathcal{X})$$ , where $$mathcal{X}$$ is finite and where the interactions of x with respect to $$mathcal{X}$$ , given by $$xi (x,mathcal{X})$$ , are spatially correlated. We focus on subadditive methods and stabilization methods as a way to obtain weak laws of large numbers, variance asymptotics, and central limit theorems for normalized and re-scaled versions of $$sum _{i=1}^{n}xi (eta _{i},{eta _{j}}_{j=1}^{n})$$ , where η j , j ≥ 1, are i.i.d. random variables. The general theory is applied to deduce the limit theory for functionals arising in Euclidean combinatorial optimization, convex hulls of i.i.d. samples, random sequential packing, and dimension estimation." @default.
- W96374469 created "2016-06-24" @default.
- W96374469 creator A5077089504 @default.
- W96374469 date "2012-10-13" @default.
- W96374469 modified "2023-09-26" @default.
- W96374469 title "Limit Theorems in Discrete Stochastic Geometry" @default.
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- W96374469 doi "https://doi.org/10.1007/978-3-642-33305-7_8" @default.
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