Werner's Measure on Self-Avoiding Loops and Welding
Werner's conformally invariant family of measures on self-avoiding loops on Riemann surfaces is determined by a single measure μ0 on self-avoiding loops in C∖{0} which surround 0. Our first major objective is to show that the measure μ0 is infinitesimally invariant with respect to conformal vec...
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| Дата: | 2014 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2014
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146622 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Werner's Measure on Self-Avoiding Loops and Welding / A. Chavez, D. Pickrell // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 17 назв. — англ. |
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irk-123456789-1466222019-02-11T01:24:18Z Werner's Measure on Self-Avoiding Loops and Welding Chavez, A. Pickrell, D. Werner's conformally invariant family of measures on self-avoiding loops on Riemann surfaces is determined by a single measure μ0 on self-avoiding loops in C∖{0} which surround 0. Our first major objective is to show that the measure μ0 is infinitesimally invariant with respect to conformal vector fields (essentially the Virasoro algebra of conformal field theory). This makes essential use of classical variational formulas of Duren and Schiffer, which we recast in representation theoretic terms for efficient computation. We secondly show how these formulas can be used to calculate (in principle, and sometimes explicitly) quantities (such as moments for coefficients of univalent functions) associated to the conformal welding for a self-avoiding loop. This gives an alternate proof of the uniqueness of Werner's measure. We also attempt to use these variational formulas to derive a differential equation for the (Laplace transform of) the ''diagonal distribution'' for the conformal welding associated to a loop; this generalizes in a suggestive way to a deformation of Werner's measure conjectured to exist by Kontsevich and Suhov (a basic inspiration for this paper). 2014 Article Werner's Measure on Self-Avoiding Loops and Welding / A. Chavez, D. Pickrell // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 17 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 60D05; 60B15; 17B68; 30C99 DOI:10.3842/SIGMA.2014.081 http://dspace.nbuv.gov.ua/handle/123456789/146622 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Werner's conformally invariant family of measures on self-avoiding loops on Riemann surfaces is determined by a single measure μ0 on self-avoiding loops in C∖{0} which surround 0. Our first major objective is to show that the measure μ0 is infinitesimally invariant with respect to conformal vector fields (essentially the Virasoro algebra of conformal field theory). This makes essential use of classical variational formulas of Duren and Schiffer, which we recast in representation theoretic terms for efficient computation. We secondly show how these formulas can be used to calculate (in principle, and sometimes explicitly) quantities (such as moments for coefficients of univalent functions) associated to the conformal welding for a self-avoiding loop. This gives an alternate proof of the uniqueness of Werner's measure. We also attempt to use these variational formulas to derive a differential equation for the (Laplace transform of) the ''diagonal distribution'' for the conformal welding associated to a loop; this generalizes in a suggestive way to a deformation of Werner's measure conjectured to exist by Kontsevich and Suhov (a basic inspiration for this paper). |
| format |
Article |
| author |
Chavez, A. Pickrell, D. |
| spellingShingle |
Chavez, A. Pickrell, D. Werner's Measure on Self-Avoiding Loops and Welding Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Chavez, A. Pickrell, D. |
| author_sort |
Chavez, A. |
| title |
Werner's Measure on Self-Avoiding Loops and Welding |
| title_short |
Werner's Measure on Self-Avoiding Loops and Welding |
| title_full |
Werner's Measure on Self-Avoiding Loops and Welding |
| title_fullStr |
Werner's Measure on Self-Avoiding Loops and Welding |
| title_full_unstemmed |
Werner's Measure on Self-Avoiding Loops and Welding |
| title_sort |
werner's measure on self-avoiding loops and welding |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146622 |
| citation_txt |
Werner's Measure on Self-Avoiding Loops and Welding / A. Chavez, D. Pickrell // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 17 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:25:14Z |
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