Sharp thresholds and percolation in the plane
Recently, the authors showed that the critical probability for random Voronoi percolation in the plane is 1/2. A by-product of the method was a short proof of the Harris-Kesten Theorem concerning bond percolation in the planar square lattice. The aim of this paper is to show that the same techniques...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2004
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| _version_ | 1826283974987612160 |
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| author | Bollobas, B Riordan, O |
| author_facet | Bollobas, B Riordan, O |
| author_sort | Bollobas, B |
| collection | OXFORD |
| description | Recently, the authors showed that the critical probability for random Voronoi percolation in the plane is 1/2. A by-product of the method was a short proof of the Harris-Kesten Theorem concerning bond percolation in the planar square lattice. The aim of this paper is to show that the same techniques can be applied to many other planar percolation models, both to obtain short proofs of known results, and to prove new ones. |
| first_indexed | 2024-03-07T01:06:54Z |
| format | Journal article |
| id | oxford-uuid:8ba7d011-3e68-4ca4-982c-8cacb5090b95 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:06:54Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | oxford-uuid:8ba7d011-3e68-4ca4-982c-8cacb5090b952022-03-26T22:39:30ZSharp thresholds and percolation in the planeJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:8ba7d011-3e68-4ca4-982c-8cacb5090b95EnglishSymplectic Elements at Oxford2004Bollobas, BRiordan, ORecently, the authors showed that the critical probability for random Voronoi percolation in the plane is 1/2. A by-product of the method was a short proof of the Harris-Kesten Theorem concerning bond percolation in the planar square lattice. The aim of this paper is to show that the same techniques can be applied to many other planar percolation models, both to obtain short proofs of known results, and to prove new ones. |
| spellingShingle | Bollobas, B Riordan, O Sharp thresholds and percolation in the plane |
| title | Sharp thresholds and percolation in the plane |
| title_full | Sharp thresholds and percolation in the plane |
| title_fullStr | Sharp thresholds and percolation in the plane |
| title_full_unstemmed | Sharp thresholds and percolation in the plane |
| title_short | Sharp thresholds and percolation in the plane |
| title_sort | sharp thresholds and percolation in the plane |
| work_keys_str_mv | AT bollobasb sharpthresholdsandpercolationintheplane AT riordano sharpthresholdsandpercolationintheplane |