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An algorithm for calculating critical probabilities and percolation functions in percolation models defined by rotations

Published online by Cambridge University Press:  19 September 2008

Ronald W. J. Meester
Ronald W. J. Meester
Affiliation:
Faculty of Technical Mathematics and Informatics, Delft University of Technology, Julianalaan 132, 2628 BL Delft, The Netherlands
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Abstract

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A class of percolation models on ℤd is developed in which the stochastic structure is provided by means of a d-parameter dynamical system. Of particular interest are those models generated by circle rotations. Unlike for independent models, the critical value and the percolation function can be explicitly calculated. These calculations lead to a conjecture concerning the behaviour of a related dynamical system.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 9 , Issue 3 , September 1989 , pp. 495 - 509
Copyright
Copyright © Cambridge University Press 1989

References

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