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Journal article

Subcritical $ \mathcal{U}$-bootstrap percolation models have non-trivial phase transitions

Abstract:: We prove that there exist natural generalizations of the classical bootstrap percolation model on andZopf;² that have non-trivial critical probabilities, and moreover we characterize all homogeneous, local, monotone models with this property.

Van Enter [28] (in the case d = r = 2) and Schonmann [25] (for all d andge; r andge; 2) proved that r-neighbour bootstrap percolation models have trivial critical probabilities on andZopf;^d for e...
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Publication status:: Published

Peer review status:: Peer reviewed

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APA Style

Balister, P., Bollobás, B., Przykucki, M., & Smith, P. (2016). Subcritical $ \mathcal{U}$-bootstrap percolation models have non-trivial phase transitions. Transactions of the American Mathematical Society, 368(10), 7385–7411.

MLA Style

Balister, P., et al. “Subcritical $ \Mathcal{U}$-Bootstrap Percolation Models Have Non-Trivial Phase Transitions.” Transactions of the American Mathematical Society, vol. 368, no. 10, American Mathematical Society, 2016, pp. 7385–411.

Chicago Style

Balister, P, B Bollobás, M Przykucki, and P Smith. 2016. “Subcritical $ \Mathcal{U}$-Bootstrap Percolation Models Have Non-Trivial Phase Transitions.” Transactions of the American Mathematical Society 368 (10): 7385–7411.
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Files:: TRAN6586.pdf

(Accepted manuscript, pdf, 423.8KB)

Publisher copy:: 10.1090/tran/6586

Authors

+ Balister, P More by this author

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Author

+ Bollobás, B More by this author

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Author

+ Przykucki, M More by this author

Institution:

University of Oxford

Division:

MPLS

Department:

Mathematical Institute

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+ Smith, P More by this author

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Author

Bibliographic Details

Publisher:: American Mathematical Society Publisher's website
Journal:: Transactions of the American Mathematical Society Journal website
Volume:: 368
Issue:: 10
Pages:: 7385-7411
Publication date:: 2016-01-27
DOI:: 10.1090/tran/6586
EISSN:: 1088-6850
ISSN:: 0002-9947

Item Description

Keywords:: Bootstrap percolation

phase transitions
Pubs id:: pubs:611171
UUID:: uuid:1314dca7-f2e9-4f64-aa5b-634f1504f291
Local pid:: pubs:611171
Source identifiers:: 611171
Deposit date:: 2016-03-21

Terms of use

Copyright holder:: American Mathematical Society
Copyright date:: 2016
Notes:: Copyright 2016 American Mathematical Society.

Licence:: Terms and Conditions of Use for Oxford University Research Archive

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