Tsukuda, Koji Functional central limit theorems in \(L^{2}(0,1)\) for logarithmic combinatorial assemblies. (English) Zbl 1429.60034 Bernoulli 24, No. 2, 1033-1052 (2018). 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. Cited in 2 Documents MSC: 60F17 Functional limit theorems; invariance principles 60C05 Combinatorial probability 60F05 Central limit and other weak theorems Keywords:functional central limit theorem; logarithmic assembly; Poisson approximation; random mappings; Ewens sampling formula PDFBibTeX XMLCite \textit{K. Tsukuda}, Bernoulli 24, No. 2, 1033--1052 (2018; Zbl 1429.60034) Full Text: DOI Euclid