On the value of the critical point in fractal percolation (Q2746212)
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scientific article; zbMATH DE number 1655642
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the value of the critical point in fractal percolation |
scientific article; zbMATH DE number 1655642 |
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On the value of the critical point in fractal percolation (English)
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10 October 2001
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fractal percolation
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critical probability
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The author derives a new lower bound for the critical probability \(p_c\) of Mandelbrot's dyadic fractal percolation model. For it he adds to the random fractal set a deterministic set, which simplifies the connectivity structure and whose critical probability \(p_c'\) can be computed explicitly with a simple computer program, giving the value \(p_c'= 0.811\). Rigorously he proves \(p_c' > 0.8107\), which thus is also a lower bound for \(p_c\).
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