Quadri-tilings of the plane
| dc.creator | de Tilière, B. | |
| dc.date | 2004-03-19 | |
| dc.date | 2006-05-22 | |
| dc.date.accessioned | 2026-07-07T12:40:02Z | |
| dc.date.available | 2026-07-07T12:40:02Z | |
| dc.description | We introduce {\em quadri-tilings} and show that they are in bijection with dimer models on a {\em family} of graphs $\{R^*\}$ arising from rhombus tilings. Using two height functions, we interpret a sub-family of all quadri-tilings, called {\em triangular quadri-tilings}, as an interface model in dimension 2+2. Assigning "critical" weights to edges of $R^*$, we prove an explicit expression, only depending on the local geometry of the graph $R^*$, for the minimal free energy per fundamental domain Gibbs measure; this solves a conjecture of \cite{Kenyon1}. We also show that when edges of $R^*$ are asymptotically far apart, the probability of their occurrence only depends on this set of edges. Finally, we give an expression for a Gibbs measure on the set of {\em all} triangular quadri-tilings whose marginals are the above Gibbs measures, and conjecture it to be that of minimal free energy per fundamental domain. | |
| dc.description | Revised version, minor changes. 30 pages, 13 figures | |
| dc.identifier | https://arxiv.org/abs/math/0403324 | |
| dc.identifier | http://arxiv.org/abs/math/0403324 | |
| dc.identifier | Probab. Theory Related Fields 137 (2007), no. 3-4, 487--518 | |
| dc.identifier | doi:10.1007/s00440-006-0002-9 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/219326 | |
| dc.subject | Probability | |
| dc.subject | 82B20 | |
| dc.title | Quadri-tilings of the plane | |
| dc.type | text |