Enhanced interface repulsion from quenched hard-wall randomness
| dc.creator | Bertacchi, Daniela | |
| dc.creator | Giacomin, Giambattista | |
| dc.date | 2001-12-20 | |
| dc.date.accessioned | 2026-07-07T04:45:24Z | |
| dc.date.available | 2026-07-07T04:45:24Z | |
| dc.description | We consider the harmonic crystal on the d-dimensional lattice, d larger or equal to 3, that is the centered Gaussian field $ϕ$ with covariance given by the Green function of the simple random walk on $Z^d$. Our main aim is to obtain quantitative information on the repulsion phenomenon that arises when we condition the field to be larger than an IID field $σ$ (which is also independent of $ϕ$), for every x in a large region $D_N=ND\cap \Z^d$, with N a positive integer and $D \subset\R^d$. We are mostly motivated by results for given typical realizations of the $σ$ (quenched set-up), since the conditioned harmonic crystal may be seen as a model for an equilibrium interface, constrained not to go below a inhomogeneous substrate that acts as a hard wall. We consider various types of substrate and we observe that the interface is pushed away from the wall much more than in the case of a flat wall as soon as the upward tail of $σ$ is heavier than Gaussian, while essentially no effect is observed if the tail is sub--Gaussian. In the critical case, that is the one of approximately Gaussian tail, the interplay of the two sources of randomness, $ϕ$ and $σ$, leads to an enhanced repulsion effect of additive type. | |
| dc.description | 28 pages | |
| dc.identifier | https://arxiv.org/abs/math/0112225 | |
| dc.identifier | http://arxiv.org/abs/math/0112225 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62941 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 82B24; 60K35; 60G15 | |
| dc.title | Enhanced interface repulsion from quenched hard-wall randomness | |
| dc.type | text |