A conformally invariant metric on CLE(4)
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About this item
| Description: |
Watson, S (Massachusetts Institute of Technology)
Tuesday 27 January 2015, 13:30-14:30 |
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| Created: | 2015-02-02 12:35 |
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| Collection: | Random Geometry |
| Publisher: | Isaac Newton Institute |
| Copyright: | Watson, S |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
|
| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | Co-authors: Scott Sheffield (MIT), Hao Wu (MIT)
Werner and Wu introduced a conformally invariant way of exploring the loops in a CLE4 Γ in a simply connected domain. Using the relationship between CLE4 and the Gaussian free field, we show that the dynamics of this exploration process are a deterministic function of the CLE4 loops, and we use this fact to construct a conformally invariant metric on Γ for which a ball of radius t coincides with the set of loops explored up to time t by the exploration process. It is conjectured that this metric space is related in the ϵ→0 limit to the contact graph metric on CLE4+ϵ as well as the contact graph metric on ϵ-neighborhoods of CLE4 loops. |
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