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Energy of flows on Z2 percolation clusters

โœ Scribed by Christopher Hoffman

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
141 KB
Volume
16
Category
Article
ISSN
1042-9832

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โœฆ Synopsis

We show that if p > p c Z 2 , then the unique infinite percolation cluster supports a nonzero flow f with finite q energy for all q > 2. This extends the work of Grimmett, Kesten, and Zhang (Probab Th. Relat Fields 96 (1993), 33-44) and Levin and Peres (Preprint, 1998) in dimensions d โ‰ฅ 3. As an application of our techniques we exhibit a graph that has transient percolation clusters, but does not admit exponential intersection tails. This answers a question asked by

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โœ Filip V. Babalievski ๐Ÿ“‚ Article ๐Ÿ“… 1992 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 266 KB

Two different approaches to the parallelization of percolation cluster Monte Carlo simulations are briefly discussed. Suggestions for modifying these methods as to comprise the percolation transport problem and the cluster-flip dynamics are offered.