Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Bootstrap Percolation

  • Paolo De Gregorio
  • Aonghus Lawlor
  • Kenneth A. Dawson
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_41-3

Definition of the Subject

In bootstrap percolation, we start with a lattice configuration of occupied and vacant sites. Occupied sites that have less than a certain prescribed number of occupied neighbors are rendered vacant, and as new occupied sites are found to satisfy the same condition, these are also rendered vacant. The process is iterated until eventually no more sites can be removed (if any exist). Bootstrap percolation endeavors to determine whether any occupied sites will survive the culling process and what the macroscopic geometrical properties of the occupied ensembles are. In essence, it is a generalization of conventional percolation which has led to many fruitful insights. A complementary view, which emphasizes the dynamical aspect of the bootstrap process, treats the vacant sites as invasive units and occupied sites as inert ones. Inert sites that are surrounded by too many invasive sites will become irreversibly infected and will start themselves to invade others. At...


System Size Vacant Site Regular Lattice Cayley Tree Occupied Site 
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© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Paolo De Gregorio
    • 1
  • Aonghus Lawlor
    • 2
  • Kenneth A. Dawson
    • 2
  1. 1.Dipartimento di Fisica e Astronomia, Università di PadovaINFN. Sezione di PadovaPadovaItaly
  2. 2.School of Chemistry and Chemical BiologyUniversity College DublinDublinIreland