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Functional central limit theorems in \(L^{2}(0,1)\) for logarithmic combinatorial assemblies. (English) Zbl 1429.60034

Summary: Functional central limit theorems in \(L^{2}(0,1)\) for logarithmic combinatorial assemblies are presented. The random elements argued in this paper are viewed as elements taking values in \(L^{2}(0,1)\) whereas the Skorokhod space is argued as a framework of weak convergences in functional central limit theorems for random combinatorial structures in the literature. It enables us to treat other standardized random processes which converge weakly to a corresponding Gaussian process with additional assumptions.

MSC:

60F17 Functional limit theorems; invariance principles
60C05 Combinatorial probability
60F05 Central limit and other weak theorems
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