Abstract
Random structures have an intricate relationship with the random walks defined on them. Here we focus on random walks on percolation clusters as a prime example of the random conductance model with the additional charm of not being elliptic. We discuss random walks on supercritical percolation clusters, on finite critical clusters, and on the incipient infinite cluster. The results show that random walks on supercritical and critical percolation structures behave completely differently, underlining the remarkable features of critical structures.
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Notes
- 1.
We do not use \(\tau \) for risk of confusion with the two-point function that appears so prominently in this text.
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© 2017 Springer International Publishing Switzerland
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Heydenreich, M., van der Hofstad, R. (2017). Random Walks on Percolation Clusters. In: Progress in High-Dimensional Percolation and Random Graphs. CRM Short Courses. Springer, Cham. https://doi.org/10.1007/978-3-319-62473-0_14
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DOI: https://doi.org/10.1007/978-3-319-62473-0_14
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-62472-3
Online ISBN: 978-3-319-62473-0
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