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- YVAN VELENIK
- 2003

We derive precise Ornstein-Zernike asymptotic formula for the decay of the two-point function σ0σx β in the general context of finite range Ising type models on Z d. The proof relies in an essential way on the a-priori knowledge of the strict exponential decay of the two-point function and, by the sharp characterization of phase transition due to Aizenman,… (More)

We study the distribution of cycle lengths in models of nonuniform random permutations with cycle weights. We identify several regimes. Depending on the weights, the length of typical cycles grows like the total number n of elements, or a fraction of n, or a logarithmic power of n.

- Erwin Bolthausen, Yvan Velenik
- 2008

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)

- T Bodineau, D Ioffe, Y Velenik
- 2000

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)

- Yvan Velenik
- 1996

We give a mathematical theory of the wetting phenomenon in the 2D Ising model using the formalism of Gibbs states. We treat the grand canonical and canonical ensembles.

- Yvan Velenik
- 2005

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)

- J.-D Deuschel, Yvan Velenik
- 2000

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)

- C.-E Ppster, Y Velenik
- 1997

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)

- Yvan Velenik
- 2006

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)