Achlioptas processes can be nonconvergent

Details Achlioptas processes can be nonconvergent Achlioptas processes can be nonconvergent

2011-11-26

arxiv.org/abs/1111.6177v1

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.

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