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2021 Stochastic block model in a new critical regime and the interacting multiplicative coalescent
Vitalii Konarovskyi, Vlada Limic
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Electron. J. Probab. 26: 1-23 (2021). DOI: 10.1214/21-EJP584


This work exhibits a novel phase transition for the classical stochastic block model (SBM). In addition we study the SBM in the corresponding near-critical regime, and find the scaling limit for the component sizes. The two-parameter stochastic process arising in the scaling limit, an analogue of the standard Aldous’ multiplicative coalescent, is interesting in its own right. We name it the (standard) Interacting Multiplicative Coalescent. To the best of our knowledge, this object has not yet appeared in the literature.


The first author is very grateful to the Mathematics Department at the University of Strasbourg for their hospitality and for providing him with a friendly and stimulating work environment during his visit in February and March 2020. We wish to thank the anonymous referee for their careful reading of the paper, and in particular for spotting an important gap and a mistake in the previous arguments in Section 2.


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Vitalii Konarovskyi. Vlada Limic. "Stochastic block model in a new critical regime and the interacting multiplicative coalescent." Electron. J. Probab. 26 1 - 23, 2021.


Received: 27 March 2020; Accepted: 10 January 2021; Published: 2021
First available in Project Euclid: 23 March 2021

arXiv: 2003.10958
Digital Object Identifier: 10.1214/21-EJP584

Primary: 05C80 , 60B12 , 60J75 , 60K35

Keywords: multiplicative coalescent , near-critical , phase transition , random graph , Stochastic block model

Vol.26 • 2021
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