Alignment percolation
| Autor: | Beaton, Nicholas R., Grimmett, Geoffrey R., Holmes, Mark |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s11040-021-09373-7 |
| Popis: | The existence (or not) of infinite clusters is explored for two stochastic models of intersecting line segments in $d \ge 2$ dimensions. Salient features of the phase diagram are established in each case. The models are based on site percolation on ${\mathbb Z}^d$ with parameter $p\in (0,1]$. For each occupied site $v$, and for each of the $2d$ possible coordinate directions, declare the entire line segment from $v$ to the next occupied site in the given direction to be either blue or not blue according to a given stochastic rule. In the one-choice model, each occupied site declares one of its $2d$ incident segments to be blue. In the independent model, the states of different line segments are independent. Comment: Accepted version: Mathematical Physics, Algebra and Geometry |
| Databáze: | arXiv |
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