Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2011-11-26
Physics
Condensed Matter
Statistical Mechanics
4 pages, 3 figures
Scientific paper
The `explosive percolation' phenomenon has recently received considerable attention from mathematicians and physicists. For certain Achlioptas processes (`local' modifications of the classical Erd\H{o}s--R\'enyi random graph process) the key question is whether the scaling limit is discontinuous at the percolation threshold or not. Much of the time the scaling limit is assumed to exist without further comment. We show that this assumption is not justified in general: there are natural examples of Achlioptas processes with no deterministic scaling limit.
Riordan Oliver
Warnke Lutz
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