Abstract
A bootstrap percolation process on a graph with infection threshold
Critical phenomena in bootstrap percolation processes were originally observed by Aizenman and Lebowitz in the late 1980s as finite-volume phase transitions in
The main results of this paper determine those weight sequences for which a critical phenomenon occurs: there is a critical density of vertices that are infected at the beginning of the process, above which a small (sublinear) set of infected vertices creates an avalanche of infections that in turn leads to an outbreak. We show that this occurs essentially only when the tail of the weight distribution dominates a power law with exponent 3 and we determine the critical density in this case.
Citation
Nikolaos Fountoulakis. Mihyun Kang. Christoph Koch. Tamás Makai. "A phase transition regarding the evolution of bootstrap processes in inhomogeneous random graphs." Ann. Appl. Probab. 28 (2) 990 - 1051, April 2018. https://doi.org/10.1214/17-AAP1324
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