## Bernoulli

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

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

#### 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