@article{c2d19f0fc2ad461bb0ea54be2fd95223,

title = "Random connection models in the thermodynamic regime: central limit theorems for add-one cost stabilizing functionals",

abstract = "The paper deals with a random connection model, a random graph whose vertices are given by a homogeneous Poisson point process on Rd, and edges are independently drawn with probability depending on the locations of the two end points. We establish central limit theorems (CLT) for general functionals on this graph under minimal assumptions that are a combination of the weak stabilization for the add-one cost and a (2 + δ)-moment condition. As a consequence, CLTs for isomorphic subgraph counts, isomorphic component counts, the number of connected components are then derived. In addition, CLTs for Betti numbers and the size of the largest component are also proved for the first time.",

keywords = "Betti numbers, Central limit theorem, Clique complex, Random connection model, Weak stabilization",

author = "Can, {Van Hao} and Trinh, {Khanh Duy}",

note = "Funding Information: *Khanh Duy Trinh is partially supported by JST CREST Mathematics (15656429) and JSPS KAKENHI Grant Number JP19K14547. The work of Van Hao Can is supported by the Singapore Ministry of Education Academic Research Fund Tier 2 Grant MOE2018-T2-2-076, and Vietnam Academy of Science and Technology Grant CTTH00.02/22-23. †Department of Statistics and Data Science, National University of Singapore. ‡Institute of Mathematics, Vietnam Academy of Science and Technology. E-mail: cvhao89@gmail.com §Global Center for Science and Engineering, Waseda University, Japan. E-mail: trinh@aoni.waseda.jp Publisher Copyright: {\textcopyright} 2022, Institute of Mathematical Statistics. All rights reserved.",

year = "2022",

doi = "10.1214/22-EJP759",

language = "English",

volume = "27",

journal = "Electronic Journal of Probability",

issn = "1083-6489",

publisher = "Institute of Mathematical Statistics",

}