Bootstrap percolation on the stochastic block model

Autor:	Giovanni Luca Torrisi, Michele Garetto, Emilio Leonardi
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	Statistics and Probability Performance (cs.PF) FOS: Computer and information sciences Bootstrap percolation Random Graphs Stochastic Block Model Phase transition Computer Science - Performance 60K35 05C80 Probability (math.PR) FOS: Mathematics Mathematics - Probability
Popis:	We analyze the bootstrap percolation process on the stochastic block model (SBM), a natural extension of the Erd\H{o}s--R\'{e}nyi 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. Comment: 36 pages, 7 figures. arXiv admin note: text overlap with arXiv:1812.09107
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7edf5865160c4f0dbd54c9a6b6d4eb7f https://hdl.handle.net/2318/1893723 Zobrazit plný text záznamu