Year: 2025
Type: article
Abstract: We study a parametrized family of discrete time network evolution models. The evolution of the graph is based on constructions and deletions of k-cliques. Using martingale theory, we prove an almost sure limit theorem for the number of vertices, then show its asymptotic normality. We obtain an almost sure limit theorem for the degree of a fixed vertex. We also present an asymptotic normality result for the degree of a fixed vertex. Functional limit theorem is obtained for the number of vertices. Multidimensional functional limit theorem is proved for the joint behaviour of the degrees of several fixed vertices. For the proof, we apply martingale functional limit theorems. Besides mathematical proofs, we offer simulation results supporting our theorems.
Source: Statistical Papers
Authors: István Fazekas, László Fórián
Institution: University of Debrecen
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,890
Funder: Debreceni Egyetem
OpenAlex ID: W4411131709