%0 Journal Article %1 Riordan2012Achlioptas %A Riordan, Oliver %A Warnke, Lutz %D 2012 %I American Physical Society %J Physical Review E %K self-averaging percolation explosive-percolation %P 011129+ %R 10.1103/physreve.86.011129 %T Achlioptas processes are not always self-averaging %U http://dx.doi.org/10.1103/physreve.86.011129 %V 86 %X We consider a class of percolation models, called Achlioptas processes, discussed in Science 323 1453 (2009) and Science 333 322 (2011). For these, the evolution of the order parameter (the rescaled size of the largest connected component) has been the main focus of research in recent years. We show that, in striking contrast to ” classical” models, self-averaging is not a universal feature of these new percolation models: there are natural Achlioptas processes whose order parameter has random fluctuations that do not disappear in the thermodynamic limit.

@article{Riordan2012Achlioptas, abstract = {{We consider a class of percolation models, called Achlioptas processes, discussed in Science 323 1453 (2009) and Science 333 322 (2011). For these, the evolution of the order parameter (the rescaled size of the largest connected component) has been the main focus of research in recent years. We show that, in striking contrast to ” classical” models, self-averaging is not a universal feature of these new percolation models: there are natural Achlioptas processes whose order parameter has random fluctuations that do not disappear in the thermodynamic limit.}}, added-at = {2019-06-10T14:53:09.000+0200}, author = {Riordan, Oliver and Warnke, Lutz}, biburl = {https://www.bibsonomy.org/bibtex/21b2ed3380ad904aaebe56bad3adaffd8/nonancourt}, citeulike-article-id = {10988097}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/physreve.86.011129}, citeulike-linkout-1 = {http://link.aps.org/abstract/PRE/v86/i1/e011129}, citeulike-linkout-2 = {http://link.aps.org/pdf/PRE/v86/i1/e011129}, doi = {10.1103/physreve.86.011129}, interhash = {a82b7464f686c68b72d30979054c613d}, intrahash = {1b2ed3380ad904aaebe56bad3adaffd8}, journal = {Physical Review E}, keywords = {self-averaging percolation explosive-percolation}, month = jul, pages = {011129+}, posted-at = {2012-09-17 12:07:56}, priority = {2}, publisher = {American Physical Society}, timestamp = {2019-08-01T16:09:32.000+0200}, title = {{Achlioptas processes are not always self-averaging}}, url = {http://dx.doi.org/10.1103/physreve.86.011129}, volume = 86, year = 2012 }