DENSE MULTIGRAPHON-VALUED STOCHASTIC PROCESSES AND EDGE-CHANGING DYNAMICS IN THE CONFIGURATION MODEL

Röllin，Adrian1; Zhang，Zhuo Song2

2023-08-01

10.1214/22-AAP1889

Annals of Applied Probability   Impact Factor & Quartile

1050-5164

Time-evolving random graph models have appeared and have been studied in various fields of research over the past decades. However, the rigorous mathematical treatment of large graphs and their limits at the process-level is still in its infancy. In this article, we adapt the approach of Athreya, den Hollander and Röllin (Ann. Appl. Probab. 31 (2021) 1724–1745) to the setting of multigraphs and multigraphons, introduced by Kolossváry and Ráth (Acta Math. Hungar. 130 (2011) 1–34). We then generalise the work of Ráth (Random Structures Algorithms 41 (2012) 365–390) and Ráth and Szakács (Acta Math. Hungar. 136 (2012) 196–221), who analysed edge-flipping dynamics on the configuration model—in contrast to their work, we establish weak convergence at the process-level, and by allowing removal and addition of edges, these limits are nondeterministic.

configuration random multigraph model dense multigraph sequences edge-reconnection model Graphons

SCI

English

Others

Ministry of Education - Singapore[MOE2018-T2-2-076];

Mathematics

Statistics & Probability

WOS:001031710500019

INST MATHEMATICAL STATISTICS-IMS

MATHEMATICS

2-s2.0-85166041956

Scopus

1.Department of Statistics and Data Science,National University of Singapore,Singapore
2.Department of Statistics and Data Science,Southern University of Science and Technology,China

Röllin，Adrian,Zhang，Zhuo Song. DENSE MULTIGRAPHON-VALUED STOCHASTIC PROCESSES AND EDGE-CHANGING DYNAMICS IN THE CONFIGURATION MODEL[J]. Annals of Applied Probability,2023,33(4):3207-3239.

Röllin，Adrian,&Zhang，Zhuo Song.(2023).DENSE MULTIGRAPHON-VALUED STOCHASTIC PROCESSES AND EDGE-CHANGING DYNAMICS IN THE CONFIGURATION MODEL.Annals of Applied Probability,33(4),3207-3239.

Röllin，Adrian,et al."DENSE MULTIGRAPHON-VALUED STOCHASTIC PROCESSES AND EDGE-CHANGING DYNAMICS IN THE CONFIGURATION MODEL".Annals of Applied Probability 33.4(2023):3207-3239.