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Probability Theory and Related Fields

, Volume 90, Issue 3, pp 291–300 | Cite as

Phase transitions in Mandelbrot's percolation process in three dimensions

  • J. T. Chayes
  • L. Chayes
  • E. Grannan
  • G. Swindle
Article

Summary

We study the phase structure and transitions in three-dimensional Mandelbrot percolation—a process which generates random fractal sets. We establish the existence of three distinct phase transitions, and we show that two of these transitions, corresponding to percolation across the initial set by paths and sheets, are discontinuous.

Keywords

Phase Transition Stochastic Process Probability Theory Phase Structure Mathematical Biology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • J. T. Chayes
    • 1
  • L. Chayes
    • 1
  • E. Grannan
    • 2
  • G. Swindle
    • 3
  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA
  2. 2.AT & T Bell LaboratoriesMurray HillUSA
  3. 3.Department of Statistics and Applied ProbabilityUniversity of CaliforniaSanta BarbaraUSA

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