Height fluctuations in the honeycomb dimer model
| dc.creator | Kenyon, Richard | |
| dc.date | 2004-05-19 | |
| dc.date | 2007-05-29 | |
| dc.date.accessioned | 2026-07-07T08:05:56Z | |
| dc.date.available | 2026-07-07T08:05:56Z | |
| dc.description | We study a model of random surfaces arising in the dimer model on the honeycomb lattice. For a fixed ``wire frame'' boundary condition, as the lattice spacing $ε\to0$, Cohn, Kenyon and Propp [CKP] showed the almost sure convergence of a random surface to a non-random limit shape $Σ_0$. In [KO], Okounkov and the author showed how to parametrize the limit shapes in terms of analytic functions, in particular constructing a natural conformal structure on them. We show here that when $Σ_0$ has no facets, for a family of boundary conditions approximating the wire frame, the large-scale surface fluctuations (height fluctuations) about $Σ_0$ converge as $ε\to0$ to a Gaussian free field for the above conformal structure. We also show that the local statistics of the fluctuations near a given point $x$ are, as conjectured in [CKP], given by the unique ergodic Gibbs measure (on plane configurations) whose slope is the slope of the tangent plane of $Σ_0$ at $x$. | |
| dc.description | 39 pages. Expanded and revised version | |
| dc.identifier | https://arxiv.org/abs/math-ph/0405052 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0405052 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130437 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Probability | |
| dc.subject | 82B20 | |
| dc.title | Height fluctuations in the honeycomb dimer model | |
| dc.type | text |