Homogenization of random quasiconformal mappings and random delauney triangulations
In this paper, we solve two problems dealing with the homogenization of random media. We show that a random quasiconformal mapping is close to an affine mapping, while a circle packing of a random Delauney triangulation is close to a conformal map, confirming a conjecture of K. Stephenson. We also s...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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International Press
2023
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| _version_ | 1797112839229407232 |
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| author | Ivrii, O Markovic, V |
| author_facet | Ivrii, O Markovic, V |
| author_sort | Ivrii, O |
| collection | OXFORD |
| description | In this paper, we solve two problems dealing with the homogenization of random media. We show that a random quasiconformal mapping is close to an affine mapping, while a circle packing of a random Delauney triangulation is close to a conformal map, confirming a conjecture of K. Stephenson. We also show that on a Riemann surface equipped with a conformal metric, a random Delauney triangulation is close to being circle packed. |
| first_indexed | 2024-03-07T08:13:00Z |
| format | Journal article |
| id | oxford-uuid:ae943f7a-b7cf-4bda-a819-36022ec879e8 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-04-09T03:55:09Z |
| publishDate | 2023 |
| publisher | International Press |
| record_format | dspace |
| spelling | oxford-uuid:ae943f7a-b7cf-4bda-a819-36022ec879e82024-03-07T14:22:43ZHomogenization of random quasiconformal mappings and random delauney triangulationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:ae943f7a-b7cf-4bda-a819-36022ec879e8EnglishSymplectic ElementsInternational Press2023Ivrii, OMarkovic, VIn this paper, we solve two problems dealing with the homogenization of random media. We show that a random quasiconformal mapping is close to an affine mapping, while a circle packing of a random Delauney triangulation is close to a conformal map, confirming a conjecture of K. Stephenson. We also show that on a Riemann surface equipped with a conformal metric, a random Delauney triangulation is close to being circle packed. |
| spellingShingle | Ivrii, O Markovic, V Homogenization of random quasiconformal mappings and random delauney triangulations |
| title | Homogenization of random quasiconformal mappings and random delauney triangulations |
| title_full | Homogenization of random quasiconformal mappings and random delauney triangulations |
| title_fullStr | Homogenization of random quasiconformal mappings and random delauney triangulations |
| title_full_unstemmed | Homogenization of random quasiconformal mappings and random delauney triangulations |
| title_short | Homogenization of random quasiconformal mappings and random delauney triangulations |
| title_sort | homogenization of random quasiconformal mappings and random delauney triangulations |
| work_keys_str_mv | AT ivriio homogenizationofrandomquasiconformalmappingsandrandomdelauneytriangulations AT markovicv homogenizationofrandomquasiconformalmappingsandrandomdelauneytriangulations |