Central limit theorems in the configuration model

AD Barbour; A Röllin

Journal article

Central limit theorems in the configuration model

AD Barbour, A Röllin

Annals of Applied Probability | INST MATHEMATICAL STATISTICS-IMS | Published : 2019

DOI: 10.1214/18-AAP1425

Abstract

We prove a general normal approximation theorem for local graph statistics in the configuration model, together with an explicit bound on the error in the approximation with respect to the Wasserstein metric. Such statistics take the form T :=v∈V Hv, where V is the vertex set, and Hv depends on a neighbourhood in the graph around v of size at most . The error bound is expressed in terms of , |V|, an almost sure bound on Hv, the maximum vertex degree dmax and the variance of T. Under suitable assumptions on the convergence of the empirical degree distributions to a limiting distribution, we deduce that the size of the giant component in the configuration model has asymptotically Gaussian fluc..

View full abstract

University of Melbourne Researchers

Andrew Barbour Author

Related Projects (4)

MEASURE-VALUED ANALYSIS OF STOCHASTIC POPULATIONS

The project aims to develop new mathematical models and tools for the rigorous analysis of very general stochastic populations that are subj..

STOCHASTIC POPULATIONS: THEORY AND APPLICATIONS

The project aims to study models of evolution and cancer development. It will produce new mathematical results and open up new applications..

Random Network Models with Applications in Biology

Complex biological systems consist of a large number of interacting agents or components, and so can be studied using mathematical random ne..

Random Discrete Structures: Approximations and Applications

The behaviour of many real world systems can be modelled by random discrete structures evolving over time. For example, the sizes of populat..

Grants

Awarded by Australian Research Council

Funding Acknowledgements

Supported in part by Australian Research Council Grants Nos. DP120102728, DP120102398, DP150101459 and DP150103588, and by their Centre of Excellence for Mathematical and Statistical Frontiers. Supported in part by NUS Research Grant R-155-000-167-112.