Rigorous confidence intervals for critical probabilities.
We use the method of Balister, Bollobás, and Walters [Random Struct. Algorithms 26, 392 (2005)] to give rigorous 99.9999% confidence intervals for the critical probabilities for site and bond percolation on the 11 Archimedean lattices. In our computer calculations, the emphasis is on simplicity and...
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| Format: | Journal article |
| Language: | English |
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2007
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| _version_ | 1797087955000492032 |
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| author | Riordan, O Walters, M |
| author_facet | Riordan, O Walters, M |
| author_sort | Riordan, O |
| collection | OXFORD |
| description | We use the method of Balister, Bollobás, and Walters [Random Struct. Algorithms 26, 392 (2005)] to give rigorous 99.9999% confidence intervals for the critical probabilities for site and bond percolation on the 11 Archimedean lattices. In our computer calculations, the emphasis is on simplicity and ease of verification, rather than obtaining the best possible results. Nevertheless, we obtain intervals of width at most 0.0005 in all cases. |
| first_indexed | 2024-03-07T02:42:57Z |
| format | Journal article |
| id | oxford-uuid:ab155b36-f226-41c9-9feb-8e5ea8ed9b34 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:42:57Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:ab155b36-f226-41c9-9feb-8e5ea8ed9b342022-03-27T03:19:28ZRigorous confidence intervals for critical probabilities.Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:ab155b36-f226-41c9-9feb-8e5ea8ed9b34EnglishSymplectic Elements at Oxford2007Riordan, OWalters, MWe use the method of Balister, Bollobás, and Walters [Random Struct. Algorithms 26, 392 (2005)] to give rigorous 99.9999% confidence intervals for the critical probabilities for site and bond percolation on the 11 Archimedean lattices. In our computer calculations, the emphasis is on simplicity and ease of verification, rather than obtaining the best possible results. Nevertheless, we obtain intervals of width at most 0.0005 in all cases. |
| spellingShingle | Riordan, O Walters, M Rigorous confidence intervals for critical probabilities. |
| title | Rigorous confidence intervals for critical probabilities. |
| title_full | Rigorous confidence intervals for critical probabilities. |
| title_fullStr | Rigorous confidence intervals for critical probabilities. |
| title_full_unstemmed | Rigorous confidence intervals for critical probabilities. |
| title_short | Rigorous confidence intervals for critical probabilities. |
| title_sort | rigorous confidence intervals for critical probabilities |
| work_keys_str_mv | AT riordano rigorousconfidenceintervalsforcriticalprobabilities AT waltersm rigorousconfidenceintervalsforcriticalprobabilities |