Abstract
In the usual Achlioptas processes the smallest clusters of a few randomly
chosen are selected for merging together at each step. The resulting
aggregation process leads to the delayed birth of a giant cluster and the
so-called explosive percolation transition showing a set anomalous features. We
explore a process with the opposite selection rule, in which the biggest
clusters of the randomly chosen merge together. We develop a theory of this
kind of percolation based on the Smoluchowsky equation, find the percolation
threshold, and describe the scaling properties of this continuous transition,
namely, the critical exponents and amplitudes, and scaling functions. We show
that, qualitatively, this transition is similar to the ordinary percolation
one, though occurring in less connected systems.
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