Central limit theorems in Random cluster and Potts Models
| dc.creator | Garet, Olivier | |
| dc.date | 2003-08-20 | |
| dc.date.accessioned | 2026-07-07T06:31:53Z | |
| dc.date.available | 2026-07-07T06:31:53Z | |
| dc.description | We prove that for q>=1, there exists r(q)<1 such that for p>r(q), the number of points in large boxes which belongs to the infinite cluster has a normal central limit behaviour under the random cluster measure phi_{p,q} on Z^d, d>=2. Particularly, we can take r(q)=p_g^* for d=2, which is commonly conjectured to be equal to p_c. These results are used to prove a q-dimensional central limit theorems relative to the fluctuation of the empirical measures for the ground Gibbs measures of the q-state Potts model at very low temperature and the Gibbs measures which reside in the convex hull of them. A similar central limit theorem is also given in the high temperature regime. Some particular properties of the Ising model are also discussed. | |
| dc.description | version du 19 aout 2003 | |
| dc.identifier | https://arxiv.org/abs/math/0308190 | |
| dc.identifier | http://arxiv.org/abs/math/0308190 | |
| dc.identifier | Mathematical Physics Electronic Journal 11 (2005) paper 4 (27 pages) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98740 | |
| dc.subject | Probability | |
| dc.subject | 60K35; 82B20; 82B43 | |
| dc.title | Central limit theorems in Random cluster and Potts Models | |
| dc.type | text |