A Central Limit Theorem for Functions on Weighted Sparse Inhomogeneous Random Graphs

by Moritz Wemheuer
Doctoral thesis
Date of Examination:2023-06-13
Date of issue:2023-07-13
Advisor:Prof. Dr. Anja Sturm
Referee:Prof. Dr. Anja Sturm
Referee:Prof. Dr. Dominic Schuhmacher
Persistent Address: http://dx.doi.org/10.53846/goediss-10004

 

 

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Abstract

English

We prove a central limit theorem for a certain class of functions on weighted sparse inhomogeneous random graphs. The proof uses a perturbative form of Stein's method and relies on a careful analysis of the local structure of the underlying sparse inhomogeneous random graphs (as the number of vertices in the graph tends to infinity), which we carry out in detail, as well as a local approximation property of the function, which is satisfied for a number of combinatorial optimisation problems. Our results extend recent work by Cao (2021, Ann. Appl. Probab. 31) for Erdős–Rényi graphs.
Keywords: inhomogeneous random graphs; weighted graphs; central limit theorem; combinatorial optimisation; Erdős–Rényi graph; Stein's method
 
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