Invariance principle for a Potts interface along a wall

平面四态Potts模型及其随机簇表示中的共形不变性

Conformal invariance of the planar four-state Potts model and its random-cluster representation

本文证明临界随机簇模型（q=4）的环在标度极限下收敛到CLE(4)，并利用Edwards-Sokal耦合推导出四态Potts模型的共形不变性。

Translation-invariance of two-dimensional Gibbsian systems of particles with internal degrees of freedom

One of the main objectives of equilibrium state statistical physics is to analyze which symmetries of an interacting particle system in equilibrium are broken or conserved. Here we present a general result on the conservation of translational symmetry for two-dimensional Gibbsian particle systems. The result applies to particles with internal degrees of freedom and fairly arbitrary interaction, including the interesting cases of discontinuous, singular, and hard core interaction. In particular we thus show the conservation of translational symmetry for the continuum Widom Rowlinson model and a…

Fluctuation theory of connectivities for subcritical random cluster models

We develop a fluctuation theory of connectivities for subcritical random cluster models. The theory is based on a comprehensive nonperturbative probabilistic 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 classical limit laws, and our construction leads to an effective random walk representation of percolation clusters. The results include a derivation of a sharp Ornstein--Zernike type asymptotic formula for two point functions, a proof of analyticity…