Localization and delocalization of random interfaces

Abstract

The probabilistic study of effective interface models has been quite active in recent years, with a particular emphasis on the effect of various external potentials (wall, pinning potential, ...) leading to localization/delocalization transitions. I review some of the results that have been obtained. In particular, I discuss pinning by a local potential, entropic repulsion and the (pre)wetting transition, both for models with continuous and discrete heights.

Published at http://dx.doi.org/10.1214/154957806000000050 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (5)

• Smoothing effect of quenched disorder on polymer depinning transitions
• Pinning of polymers and interfaces by random potentials
• Critical behavior of the massless free field at the depinning transition
• Universality of Critical Behaviour in a Class of Recurrent Random Walks
• Enhanced interface repulsion from quenched hard-wall randomness

Cited by in corpus (28)

• Recent progress on the Random Conductance Model
• Invariance principles for random walks conditioned to stay positive
• Phase coexistence of gradient Gibbs states
• Pinning and wetting transition for (1+1)-dimensional fields with Laplacian interaction
• Scaling limit for a class of gradient fields with nonconvex potentials
• Nonexistence of random gradient Gibbs measures in continuous interface models in $d=2$
• Dynamics of $(2+1)$-dimensional SOS surfaces above a wall: Slow mixing induced by entropic repulsion
• Delocalization of two-dimensional random surfaces with hard-core constraints
• Extremal inhomogeneous Gibbs states for SOS-models and finite-spin models on trees
• Potts models with a defect line
• Excursions and path functionals for stochastic processes with asymptotically zero drifts
• Exponential decay of covariances for the supercritical membrane model
• Delocalisation and absolute-value-FKG in the solid-on-solid model
• A note on the discrete Gaussian Free Field with disordered pinning on Z^d, d\geq 2
• Random walk versus random line
• Disorder and wetting transition: the pinned harmonic crystal in dimension three or larger
• On the probability of staying above a wall for the (2+1)-dimensional SOS model at low temperature
• Infinite-volume states with irreducible localization sets for gradient models on trees
• Localization, big-jump regime and the effect disorder for a class of generalized pinning models
• No phase transition for Gaussian fields with bounded spins
• Subcritical percolation with a line of defects
• Wetting of gradient fields: pathwise estimates
• Gibbs measures for HC-model with a countable set of spin values on a Cayley tree
• Typical height of the (2+1)-D Solid-on-Solid surface with pinning above a wall in the delocalized phase
• Pinning for the critical and supercritical membrane model
• Properties of the gradient squared of the discrete Gaussian free field
• Correlations of a bound interface over a random substrate
• Fixed points of an infinite dimensional operator related to Gibbs measures