Functional central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs

• 成果类型: Article; Early Access
• 署名作者: Bhamidi, Shankar; Budhiraja, Amarjit; Sakanaveeti, Akshay
• 署名单位: University of North Carolina Chapel Hill; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051; 1432-2064
• DOI: 10.1007/s00440-026-01510-z
• 发表日期: 2026-06-20
• 关键词: Inhomogeneous random graphs; Phase Transition; Functional central limit theorems; Gaussian Processes; bounded-size rules; multiplicative coalescent; PHASE-TRANSITION; spanning tree; aggregation; coagulation; excursions; models

摘要

We study inhomogeneous random graphs with a finite type space. For a natural generalization of the model as a dynamic network-valued process, the paper establishes the following results: (a) Functional central limit theorems for the infinite vector of microscopic type-densities and characterizations of the limits as infinite-dimensional conditionally Gaussian processes in a certain Banach space. (b) Functional (joint) central limit theorems for macroscopic observables of the giant component in the supercritical regime including size, surplus and number of vertices of various types in the giant component. As a corollary this provides central limit theorems for the size of the largest connected component, its surplus, and its type vector, for percolation on dense graphs obtained from a finite type Graphon. (c) Central limit theorem for the weight of the minimum spanning tree with random i.i.d. Exponential edge weights on dense graph sequences driven by an underlying finite type graphon.