Geodesics in Brownian surfaces
1 hour 3 mins,
923.11 MB,
MPEG-4 Video
640x360,
29.97 fps,
44100 Hz,
1.95 Mbits/sec
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About this item
| Description: |
Bettinelli, J (Université de Lorraine)
Thursday 29 January 2015, 10:00-11:00 |
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| Created: | 2015-02-05 14:43 |
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| Collection: | Random Geometry |
| Publisher: | Isaac Newton Institute |
| Copyright: | Bettinelli, J |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | In this talk, we introduce a class of random metric spaces called Brownian surfaces, which generalize the famous Brownian map to the case of topologies more complicated than that of the sphere. More precisely, these random surfaces arise as the scaling limit of random maps on a given surface with a boundary. We will review the known results about these rather wild random metric spaces and we will particularly focus on the geodesics starting from a uniformly chosen random point. This allow to characterize some subsets of interest in terms of geodesics and, in particular, in terms of pairs of geodesics aiming at the same point and whose concatenation forms a loop not homotopic to 0.
Our results generalize in particular the properties shown by Le Gall on geodesics in the Brownian map, although our approach is completely different. |
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