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Percolation on an infinitely generated group

Part of: Graph theory Special processes

Published online by Cambridge University Press:  20 February 2020

Agelos Georgakopoulos  and
John Haslegrave
Agelos Georgakopoulos*
Affiliation:
Mathematics Institute, University of Warwick, CoventryCV4 7AL, UK
John Haslegrave
Affiliation:
Mathematics Institute, University of Warwick, CoventryCV4 7AL, UK
*
*Corresponding author.
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Abstract

We give an example of a long range Bernoulli percolation process on a group non-quasi-isometric with ℤ, in which clusters are almost surely finite for all values of the parameter. This random graph admits diverse equivalent definitions, and we study their ramifications. We also study its expected size and point out certain phase transitions.

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 05C80: Random graphs 05C81: Random walks on graphs
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 29 , Issue 4 , July 2020 , pp. 587 - 615
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Copyright
© Cambridge University Press 2020

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Footnotes

†

Supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 639046).

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