%0 Journal Article %1 daCosta2015Inverting %A da Costa, R. A. %A Dorogovtsev, S. N. %A Goltsev, A. V. %A Mendes, J. F. F. %D 2015 %J Physical Review E %K scaling percolation explosive-percolation %N 4 %R 10.1103/PhysRevE.91.042130 %T Inverting the Achlioptas rule for explosive percolation %U http://dx.doi.org/10.1103/PhysRevE.91.042130 %V 91 %X 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.

@article{daCosta2015Inverting, 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.}}, added-at = {2019-06-10T14:53:09.000+0200}, archiveprefix = {arXiv}, author = {da Costa, R. A. and Dorogovtsev, S. N. and Goltsev, A. V. and Mendes, J. F. F.}, biburl = {https://www.bibsonomy.org/bibtex/2a77b34ab8301292f9d85ad8af36094b6/nonancourt}, citeulike-article-id = {13533011}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/PhysRevE.91.042130}, citeulike-linkout-1 = {http://arxiv.org/abs/1503.00727}, citeulike-linkout-2 = {http://arxiv.org/pdf/1503.00727}, day = 23, doi = {10.1103/PhysRevE.91.042130}, eprint = {1503.00727}, interhash = {548a95b311e4017050bd51704e5e350e}, intrahash = {a77b34ab8301292f9d85ad8af36094b6}, issn = {1550-2376}, journal = {Physical Review E}, keywords = {scaling percolation explosive-percolation}, month = apr, number = 4, posted-at = {2015-03-06 15:13:19}, priority = {2}, timestamp = {2019-08-01T16:09:32.000+0200}, title = {{Inverting the Achlioptas rule for explosive percolation}}, url = {http://dx.doi.org/10.1103/PhysRevE.91.042130}, volume = 91, year = 2015 }