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Entropic repulsion and the maximum of the two-dimensional harmonic crystal
We consider the lattice version of the free field in two dimensions (also called harmonic crystal). The main aim of the paper is to discuss quantitatively the entropic repulsion of the random surfaceExpand
Invariance principle for the random conductance model with unbounded conductances.
We study a continuous time random walk X in an environment of i.i.d. random conductances μ e ∈ [1, ∞). We obtain heat kernel bounds and prove a quenched invariance principle for X. This holds evenExpand
Limiting Curves for I.I.D. Records
We consider the concentration of measure for n i.i.d., two-dimensional random variables under the conditioning that they form a record. Under mild conditions, we show that all random variables tendExpand
Large deviations and concentration properties for ∇ϕ interface models
Abstract. We consider the massless field with zero boundary conditions outside DN≡D∩ (ℤd/N) (N∈ℤ+), D a suitable subset of ℝd, i.e. the continuous spin Gibbs measure ℙN on ℝℤd/N with HamiltonianExpand
On estimating the derivatives of symmetric diffusions in stationary random environment, with applications to ∇ϕ interface model
Abstract.We consider diffusions on ℝd or random walks on ℤd in a random environment which is stationary in space and in time and with symmetric and uniformly elliptic coefficients. We show existenceExpand
Pinning and wetting transition for (1+1)-dimensional fields with Laplacian interaction
We consider a random field $\varphi:\{1,...,N\}\to\mathbb{R}$ as a model for a linear chain attracted to the defect line $\varphi=0$, that is, the x-axis. The free law of the field is specified byExpand
Surface order large deviations for high-density percolation
SummaryWe derive surface order large deviation estimates for the volume of the largest cluster and for the volume of the largest region surrounded by a cluster of a Bernoulli percolation processExpand
Invariance principle for the random conductance model in a degenerate ergodic environment
We study a continuous time random walk, X, on Zd in an environment of random conductances taking values in (0,∞). We assume that the law of the conductances is ergodic with respect to space shifts.Expand
Entropic repulsion of the lattice free field
Consider the massless free field on thed-dimensional lattice ℤd,d≧3; that is the centered Gaussian field on with covariances given by the Green function of the simple random walk on ℤd. We show thatExpand
Recursions and tightness for the maximum of the discrete, two dimensional Gaussian Free Field
We consider the maximum of the discrete two dimensional Gaussian free field in a box, and prove the existence of a (dense) deterministic subsequence along which the maximum, centered at its mean, isExpand