A contour line of the continuum Gaussian free field
Original manuscript August 14, 2010
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Springer-Verlag
2013
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| Online Access: | http://hdl.handle.net/1721.1/80825 https://orcid.org/0000-0002-5951-4933 |
| _version_ | 1826201628953280512 |
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| author | Schramm, Oded Sheffield, Scott Roger |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Schramm, Oded Sheffield, Scott Roger |
| author_sort | Schramm, Oded |
| collection | MIT |
| description | Original manuscript August 14, 2010 |
| first_indexed | 2024-09-23T11:54:21Z |
| format | Article |
| id | mit-1721.1/80825 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:54:21Z |
| publishDate | 2013 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/808252022-10-01T06:50:51Z A contour line of the continuum Gaussian free field Schramm, Oded Sheffield, Scott Roger Massachusetts Institute of Technology. Department of Mathematics Sheffield, Scott Roger Original manuscript August 14, 2010 Consider an instance h of the Gaussian free field on a simply connected planar domain D with boundary conditions −λ on one boundary arc and λ on the complementary arc, where λ is the special constant √π/8 . We argue that even though h is defined only as a random distribution, and not as a function, it has a well-defined zero level line γ connecting the endpoints of these arcs, and the law of γ is SLE(4) . We construct γ in two ways: as the limit of the chordal zero contour lines of the projections of h onto certain spaces of piecewise linear functions, and as the only path-valued function on the space of distributions with a natural Markov property. We also show that, as a function of h, γ is “local” (it does not change when h is modified away from γ ) and derive some general properties of local sets. 2013-09-20T14:33:48Z 2013-09-20T14:33:48Z 2012-09 2012-08 Article http://purl.org/eprint/type/JournalArticle 0178-8051 1432-2064 http://hdl.handle.net/1721.1/80825 Schramm, Oded, and Scott Sheffield. “A contour line of the continuum Gaussian free field.” Probability Theory and Related Fields 157, no. 1 2 (October 16, 2013): 47-80. https://orcid.org/0000-0002-5951-4933 en_US http://dx.doi.org/10.1007/s00440-012-0449-9 Probability Theory and Related Fields Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Springer-Verlag arXiv |
| spellingShingle | Schramm, Oded Sheffield, Scott Roger A contour line of the continuum Gaussian free field |
| title | A contour line of the continuum Gaussian free field |
| title_full | A contour line of the continuum Gaussian free field |
| title_fullStr | A contour line of the continuum Gaussian free field |
| title_full_unstemmed | A contour line of the continuum Gaussian free field |
| title_short | A contour line of the continuum Gaussian free field |
| title_sort | contour line of the continuum gaussian free field |
| url | http://hdl.handle.net/1721.1/80825 https://orcid.org/0000-0002-5951-4933 |
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