Jean-Dominique Deuschel

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 process restricted to a big finite box, with sufficiently large parameter. We also establish a useful version of the isoperimetric inequality, which is the main tool of our proofs.

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 even when Eμ e = ∞.

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 that the probability, that all the spins are positive in a box of volumeNd, decays exponentially at a rate of orderNd−2 logN and compute explicitly the corresponding constant in terms of the capacity of the unit cube. The result is extended to a class of transient random walks with transition functions in the domain of the normal and α-stable law.

Pinning and wetting transition for (1+1)-dimensional fields with Laplacian interaction

We consider a random field

A Quantum Version of Sanov's Theorem

\varphi:\{1,...,N\}\to\mathbb{R}

Microcanonical distributions for lattice gases

as a model for a linear chain attracted to the defect line

Scaling limits of (1+1)-dimensional pinning models with laplacian interaction

\varphi=0

Invariance principle for the random conductance model in a degenerate ergodic environment

, that is, the x-axis. The free law of the field is specified by the density

The construction of the

\exp(-\sum_iV(\Delta\varphi_i))

(d+1)

with respect to the Lebesgue measure on