Yvan Velenik

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We consider the d-dimensional massless free field localized by a δ-pinning of strength ε. We study the asymptotics of the variance of the field (when d = 2), and of the decay-rate of its 2-point function (when d ≥ 2), as ε goes to zero, for general Gaussian interactions. Physically speaking, we thus rigorously obtain the critical behavior of the transverse(More)
The rigorous microscopic theory of equilibrium crystal shapes has made enormous progress during the last decade. We review here the main results which have been obtained, both in two and higher dimensions. In particular, we describe how the phenomenological Wulff and Winterbottom constructions can be derived from the microscopic description provided by the(More)
We report about concentration results for the measure giving the statistical properties of phase separation lines in the 2D Ising model. The results are sharp and valid for all temperatures below the critical one; they are consequences of a new approach for treating phase separation lines in the 2D Ising model and the following interesting inequality of the(More)
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 localiza-tion/delocalization transitions. I review some of the results that have been obtained. In particular, I discuss pinning by a local potential,(More)
We consider a model of a two-dimensional interface of the SOS type, with finite-range, even, strictly convex, twice continuously differentiable interactions. We prove that, under an arbitrarily weak potential favouring zero-height, the surface has finite mean square heights. We consider the cases of both square well and δ potentials. These results extend(More)
We prove existence of a wetting transition for two classes of gradient elds which include: 1) The Continuous SOS model in any dimension and 2) The Massless Gaussian model in dimension 2. Combined with a recent result proving the absence of such a transition for Gaussian models above 2 dimensions 5], this shows in particular that absolute-value and quadratic(More)
We show that a class of spin models, containing the Ashkin{Teller model, admits a generalized random{cluster (GRC) representation. Moreover we show that basic properties of the usual representation, such as FKG inequalities and comparison inequalities, still hold for this generalized random{cluster model. Some elementary consequences are given. We also(More)
We develop a fluctuation theory of connectivities for subcritical random cluster models. The theory is based on a comprehensive nonperturbative prob-abilistic description of long connected clusters in terms of essentially one-dimensional chains of irreducible objects. Statistics of local observables, for example, displacement, over such chains obey(More)