| dc.creator | Berestycki, Nathanael Edouard | |
| dc.creator | Laslier, Benoit | |
| dc.creator | Ray, Gourab | |
| dc.date.accessioned | 2017-05-12 | |
| dc.date.accessioned | 2018-11-24T23:27:22Z | |
| dc.date.available | 2017-11-09T17:05:41Z | |
| dc.date.available | 2018-11-24T23:27:22Z | |
| dc.date.issued | 2017-10-01 | |
| dc.identifier | https://www.repository.cam.ac.uk/handle/1810/268296 | |
| dc.identifier.uri | http://repository.aust.edu.ng/xmlui/handle/123456789/3970 | |
| dc.description.abstract | In this paper we consider random planar maps weighted by the self-dual Fortuin--Kasteleyn model with parameter $q \in (0,4)$. Using a bijection due to Sheffield and a connection to planar Brownian motion in a cone we obtain rigorously the value of the critical exponent associated with the length of cluster interfaces, which is shown to be $$ \frac{4}{\pi} \arccos \left( \frac{\sqrt{2 - \sqrt{q}}}{2} \right)=\frac{\kappa'}{8}. $$ where $\kappa' $ is the SLE parameter associated with this model. We also derive the exponent corresponding to the area enclosed by a loop which is shown to be 1 for all values of $q \in (0,4)$. Applying the KPZ formula we find that this value is consistent with the dimension of SLE curves and SLE duality.
Communicated by H.-T. Yau | |
| dc.publisher | Springer | |
| dc.publisher | COMMUNICATIONS IN MATHEMATICAL PHYSICS | |
| dc.rights | http://creativecommons.org/licenses/by/4.0/ | |
| dc.rights | http://creativecommons.org/licenses/by/4.0/ | |
| dc.rights | Attribution 4.0 International | |
| dc.rights | Attribution 4.0 International | |
| dc.title | Critical Exponents on Fortuin-Kasteleyn Weighted Planar Maps | |
| dc.type | Article | |
