February 2023 Bootstrap percolation on the stochastic block model
Giovanni Luca Torrisi, Michele Garetto, Emilio Leonardi
Author Affiliations +
Bernoulli 29(1): 696-724 (February 2023). DOI: 10.3150/22-BEJ1475

Abstract

We analyze the bootstrap percolation process on the stochastic block model (SBM), a natural extension of the Erdős–Rényi random graph that incorporates the community structure observed in many real systems. In the SBM, nodes are partitioned into two subsets, which represent different communities, and pairs of nodes are independently connected with a probability that depends on the communities they belong to. Under mild assumptions on the system parameters, we prove the existence of a sharp phase transition for the final number of active nodes and characterize the sub-critical and the super-critical regimes in terms of the number of initially active nodes, which are selected uniformly at random in each community.

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Giovanni Luca Torrisi. Michele Garetto. Emilio Leonardi. "Bootstrap percolation on the stochastic block model." Bernoulli 29 (1) 696 - 724, February 2023. https://doi.org/10.3150/22-BEJ1475

Information

Received: 1 November 2021; Published: February 2023
First available in Project Euclid: 13 October 2022

MathSciNet: MR4497264
zbMATH: 1515.60329
Digital Object Identifier: 10.3150/22-BEJ1475

Keywords: Bootstrap percolation , Random graphs , Stochastic block model

Vol.29 • No. 1 • February 2023
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