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  • Volume 24, Number 2 (2018), 1033-1052.

Functional central limit theorems in $L^{2}(0,1)$ for logarithmic combinatorial assemblies

Koji Tsukuda

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Abstract

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.

Article information

Source
Bernoulli, Volume 24, Number 2 (2018), 1033-1052.

Dates
Received: October 2015
First available in Project Euclid: 21 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.bj/1505980888

Digital Object Identifier
doi:10.3150/16-BEJ847

Mathematical Reviews number (MathSciNet)
MR3706786

Zentralblatt MATH identifier
06778357

Keywords
functional central limit theorem logarithmic assembly Poisson approximation random mappings the Ewens sampling formula

Citation

Tsukuda, Koji. Functional central limit theorems in $L^{2}(0,1)$ for logarithmic combinatorial assemblies. Bernoulli 24 (2018), no. 2, 1033--1052. doi:10.3150/16-BEJ847. https://projecteuclid.org/euclid.bj/1505980888


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References

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