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Analyticity results in Bernoulli percolation
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Georgakopoulos, Agelos and Panagiotis, Christoforos (2018) Analyticity results in Bernoulli percolation. (Unpublished)
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WRAP-analyticity-results-Bernoulli-percolation-Panagiotis-2018.pdf - Submitted Version - Requires a PDF viewer. Download (1289Kb) | Preview |
Abstract
We prove (rigorously) that in 2-dimensional Bernoulli percolation, the percolation density is an analytic function of the parameter in the supercritical interval. For this we introduce some techniques that have further implications. In particular, we prove that the susceptibility is analytic in the subcritical interval for all transitive short- or long-range models, and that p bond c < 1/2 for certain families of triangulations for which Benjamini & Schramm conjectured that p site c ≤ 1/2.
| Item Type: | Submitted Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Percolation (Statistical physics) | ||||||
| Official Date: | 10 September 2018 | ||||||
| Dates: |
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| Status: | Not Peer Reviewed | ||||||
| Publication Status: | Unpublished | ||||||
| RIOXX Funder/Project Grant: |
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