Abstract
We investigate some topics related to percolation where one would hope that lace-expansion ideas could prove useful, but they have not been fully explored. These topics are
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invasion percolation and its relation to minimal spanning trees,
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random walk percolation and interlacements,
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a model for a spatial complex networks denoted scale-free percolation,
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FK-percolation or random cluster model.
We hope that these lecture notes spark new interest in these topics.
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Notes
- 1.
In the literature, there are versions of this construction that do allow for cycles; this leads to a different invasion percolation cluster with the same set of vertices as our construction, but more edges.
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Heydenreich, M., van der Hofstad, R. (2017). Further Open Problems. In: Progress in High-Dimensional Percolation and Random Graphs. CRM Short Courses. Springer, Cham. https://doi.org/10.1007/978-3-319-62473-0_16
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DOI: https://doi.org/10.1007/978-3-319-62473-0_16
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-62473-0
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