The threshold regime of finite volume bootstrap percolation

By R. Cerf, F. Manzo. 2002

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Recent advances in percolation theory and its applications (2015, background): “The finite size behavior (also known as metastability) was studied in [224, 226, 227], and the threshold function was determined up to a constant factor, for all 2 ≤ k ≤ d, by Cerf and Manzo [227].”
Bootstrap percolation on the hypercube (2006, background): “For higher dimensions Cerf and Manzo [13] have obtained good upper and lower threshold functions for the board G = P d n and neighbourhood parameter r ≤ d.”
Sharp metastability threshold for two-dimensional bootstrap percolation (2002, unknown): “ar X iv :m at h/ 02 06 13 2v 1 [ m at h. PR”
The sharp threshold for bootstrap percolation in all dimensions (2010, methodology): “This technique was introduced by Cerf and Cirillo [13], and later used and reﬁned by Cerf and Manzo [14], Holroyd [32], and Balogh, Bollob´as and Morris [6].”