Phase transitions in Mandelbrot's percolation process in three dimensions |
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| Authors: | J T Chayes L Chayes E Grannan G Swindle |
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| Institution: | (1) Department of Mathematics, University of California, 90024-1555 Los Angeles, CA, USA;(2) AT & T Bell Laboratories, 07974 Murray Hill, NJ, USA;(3) Department of Statistics and Applied Probability, University of California, 93106 Santa Barbara, CA, USA |
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| Abstract: | 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.Work partially supported by NSF Grant: DMS 8806552Work partially supported by NSF Grant: DMS 8902152 |
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