L'invariance conforme et l'universalit\'e au point critique des mod\`eles bidimensionnels

  title={L'invariance conforme et l'universalit\'e au point critique des mod\`eles bidimensionnels},
  author={Yvan Saint-Aubin},
RÉSUMÉ. Des quelques articles publiés par Robert P. Langlands en physique mathématique, c’est celui publié dans le Bulletin of the American Mathematical Society sous le titre Conformal invariance in two-dimensional percolation qui a eu, à ce jour, le plus d’impact : les idées d’Oded Schramm ayant mené à l’équation de Loewner stochastique et les preuves de l’invariance conforme de modèles de physique statistique par Stanislav Smirnov ont été suscitées, au moins en partie, par cet article. Ce… 


Sharpness of the phase transition in percolation models
AbstractThe equality of two critical points — the percolation thresholdpH and the pointpT where the cluster size distribution ceases to decay exponentially — is proven for all translation invariant
Statistical Mechanics:
AbstractPROF. R. H. FOWLER'S monumental work on statistical mechanics has, in this the second edition, in his own modest words, been rearranged and brought more up to date. But the new volume is much
Scaling limits of loop-erased random walks and uniform spanning trees
AbstractThe uniform spanning tree (UST) and the loop-erased random walk (LERW) are strongly related probabilistic processes. We consider the limits of these models on a fine grid in the plane, as the
Conformal invariance in two-dimensional percolation
The word percolation, borrowed from the Latin, refers to the seeping or oozing of a liquid through a porous medium, usually to be strained. In this and related senses it has been in use since the
Finite Models for Percolation †
1. Introduction. The notion of percolation as a subject of concern to mathematicians and theoretical physicists will not be familiar to many readers of this collection; the notion of finite models of
Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model
We construct discrete holomorphic observables in the Ising model at criticality and show that they have conformally covariant scaling limits (as mesh of the lattice tends to zero). In the sequel
The Random-Cluster Model
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in
Dualität bei endlichen Modellen der Perkolation
I. Einleitung. II. Beschreibung der Modelle. A. Die Mengen und die Wahrscheinlichkeiten. B. Die Abbildungen. C. Dualitat. D. Beispiele. III. Zusatzliche theoretische Entwicklungen. A. Unregelmasiges