| Softcover ISBN: | 978-2-85629-947-0 |
| Product Code: | AST/429 |
| List Price: | $75.00 |
| AMS Member Price: | $60.00 |
| Softcover ISBN: | 978-2-85629-947-0 |
| Product Code: | AST/429 |
| List Price: | $75.00 |
| AMS Member Price: | $60.00 |
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Book DetailsAstérisqueVolume: 429; 2021; 242 ppMSC: Primary 60
The authors show that the percolation exploration path for critical \((p = 3/4)\) face percolation on a uniform random quadrangulation with simple boundary converges in the scaling limit to a certain curve-decorated metric measure space. Explicitly, the limiting object is \(SLE_{6}\) on a \(\sqrt{8/3}\)-Liouville quantum gravity (LQG) disk, or equivalently, \(SLE_{6}\) on the Brownian disk. The topology of convergence is the natural analog of the Gromov-Hausdorff topology for curve-decorated metric measure spaces. The authors also obtain analogous results for site percolation on a uniform triangulation with simple boundary. They expect that their techniques can be generalized to other variants of percolation on uniform random planar maps.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
ReadershipGraduate students and research mathematicians.
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The authors show that the percolation exploration path for critical \((p = 3/4)\) face percolation on a uniform random quadrangulation with simple boundary converges in the scaling limit to a certain curve-decorated metric measure space. Explicitly, the limiting object is \(SLE_{6}\) on a \(\sqrt{8/3}\)-Liouville quantum gravity (LQG) disk, or equivalently, \(SLE_{6}\) on the Brownian disk. The topology of convergence is the natural analog of the Gromov-Hausdorff topology for curve-decorated metric measure spaces. The authors also obtain analogous results for site percolation on a uniform triangulation with simple boundary. They expect that their techniques can be generalized to other variants of percolation on uniform random planar maps.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians.
