On central limit theorems in the random connection model

Tim van de Brug and Ronald Meester

Physica A: Statistical Mechanics and its Applications, 2004, vol. 332, issue C, 263-278

Abstract: Consider a sequence of Poisson random connection models (Xn,λn,gn) on Rd, where λn/nd→λ>0 and gn(x)=g(nx) for some non-increasing, integrable connection function g. Let In(g) be the number of isolated vertices of (Xn,λn,gn) in some bounded Borel set K, where K has non-empty interior and boundary of Lebesgue measure zero. Roy and Sarkar (Physica A 318 (2003) 1047) claim thatIn(g)−EIn(g)VarIn(g)⇝N(0,1),n→∞,where ⇝ denotes convergence in distribution. However, their proof has errors. We correct their proof and extend the result to larger components when the connection function g has bounded support.

Keywords: Central limit theorem; Percolation; Isolated points (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:332:y:2004:i:c:p:263-278

DOI: 10.1016/j.physa.2003.10.003

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