A short proof of the Harris-Kesten Theorem
We give a short proof of the fundamental result that the critical probability for bond percolation in the planar square lattice is equal to 1/2. The lower bound was proved by Harris, who showed in 1960 that percolation does not occur at $p=1/2$. The other, more difficult, bound was proved by Kesten,...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2004
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| _version_ | 1797105862380093440 |
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| author | Bollobas, B Riordan, O |
| author_facet | Bollobas, B Riordan, O |
| author_sort | Bollobas, B |
| collection | OXFORD |
| description | We give a short proof of the fundamental result that the critical probability for bond percolation in the planar square lattice is equal to 1/2. The lower bound was proved by Harris, who showed in 1960 that percolation does not occur at $p=1/2$. The other, more difficult, bound was proved by Kesten, who showed in 1980 that percolation does occur for any $p>1/2$. |
| first_indexed | 2024-03-07T06:53:24Z |
| format | Journal article |
| id | oxford-uuid:fd4a3f91-bcf5-4b11-9717-f579733d0052 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:53:24Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | oxford-uuid:fd4a3f91-bcf5-4b11-9717-f579733d00522022-03-27T13:27:54ZA short proof of the Harris-Kesten TheoremJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:fd4a3f91-bcf5-4b11-9717-f579733d0052EnglishSymplectic Elements at Oxford2004Bollobas, BRiordan, OWe give a short proof of the fundamental result that the critical probability for bond percolation in the planar square lattice is equal to 1/2. The lower bound was proved by Harris, who showed in 1960 that percolation does not occur at $p=1/2$. The other, more difficult, bound was proved by Kesten, who showed in 1980 that percolation does occur for any $p>1/2$. |
| spellingShingle | Bollobas, B Riordan, O A short proof of the Harris-Kesten Theorem |
| title | A short proof of the Harris-Kesten Theorem |
| title_full | A short proof of the Harris-Kesten Theorem |
| title_fullStr | A short proof of the Harris-Kesten Theorem |
| title_full_unstemmed | A short proof of the Harris-Kesten Theorem |
| title_short | A short proof of the Harris-Kesten Theorem |
| title_sort | short proof of the harris kesten theorem |
| work_keys_str_mv | AT bollobasb ashortproofoftheharriskestentheorem AT riordano ashortproofoftheharriskestentheorem AT bollobasb shortproofoftheharriskestentheorem AT riordano shortproofoftheharriskestentheorem |