Back to Search
Start Over
Enhanced interface repulsion from quenched hard–wall randomness
- Source :
- Probability Theory and Related Fields. 124:487-516
- Publication Year :
- 2002
- Publisher :
- Springer Science and Business Media LLC, 2002.
-
Abstract
- We consider the harmonic crystal on the d-dimensional lattice, d larger or equal to 3, that is the centered Gaussian field $\phi$ 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 $\sigma$ (which is also independent of $\phi$), 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 $\sigma$ (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 $\sigma$ 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, $\phi$ and $\sigma$, leads to an enhanced repulsion effect of additive type.<br />Comment: 28 pages
- Subjects :
- Statistics and Probability
large deviation
Field (physics)
Gaussian
FOS: Physical sciences
Geometry
82B24
60K35
60G15
quenched and annealed model
harmonic crystal
Upper and lower bounds
rough substrate
symbols.namesake
entropic repulsion
Probability theory
FOS: Mathematics
extrema of random field
Mathematical Physics
Randomness
Mathematics
Gaussian field
Random field
Probability (math.PR)
Mathematical analysis
random walks
Mathematical Physics (math-ph)
Random walk
MAT/06 - PROBABILITA E STATISTICA MATEMATICA
Bounded function
symbols
Statistics, Probability and Uncertainty
Mathematics - Probability
Analysis
Subjects
Details
- ISSN :
- 14322064 and 01788051
- Volume :
- 124
- Database :
- OpenAIRE
- Journal :
- Probability Theory and Related Fields
- Accession number :
- edsair.doi.dedup.....c7858cdc450a6c5d64138394aabcea84