相关论文: The parafermionic observable in SLE

We find discrete holomorphic parafermions of the Ashkin-Teller model on the critical line, by mapping appropriate interfaces of the model to the $O(n=1)$ model. We give support to the conjecture that the curve created by the insertion of…

We define parafermionic observables in various lattice loop models, including examples where no Kramers-Wannier duality holds. For a particular rhombic embedding of the lattice in the plane and a value of the parafermionic spin these…

These lecture notes provide a (almost) self-contained account on conformal invariance of the planar critical Ising and FK-Ising models. They present the theory of discrete holomorphic functions and its applications to planar statistical…

After a brief review of the historical role of analyticity in the study of critical phenomena, an account is given of recent discoveries of discretely holomorphic observables in critical two-dimensional lattice models. These are objects…

We introduce a notion of s-holomorphicity suitable for certain quantum spin systems in one dimension, and define two observables in the critical transverse-field Ising model which have this property. The observables are defined using…

We consider boundary conditions compatible with discrete holomorphicity for the dilute O(n) and C_2^(1) loop models. In each model, for a general set of boundary plaquettes, multiple types of loops can appear. A generalisation of Smirnov's…

An exponential Luenberger dynamical observer is proposed to estimate the state of a general class of nonautonomous semilinear parabolic equations. The result can be applied to the case where the output is given by state measurements taken…

Various features of the two-parameter family of Schramm-Loewner evolutions SLE(\kappa,\rho) are studied. In particular, we derive certain restriction properties that lead to a ``strong duality'' conjecture, which is an identity in law…

We study the discrete version of the $p$-Laplacian. Based on its variational properties we discuss some features of the associated parabolic problem. Our approach allows us in turn to obtain interesting information about positivity and…

Suppose that $\eta$ is a Schramm-Loewner evolution (SLE$_\kappa$) in a smoothly bounded simply connected domain $D \subset {\mathbb C}$ and that $\phi$ is a conformal map from ${\mathbb D}$ to a connected component of $D \setminus…

Many mathematical models of statistical physics in two dimensions are either known or conjectured to exhibit conformal invariance. Over the years, physicists proposed predictions of various exponents describing the behavior of these models.…

In empirical studies, the data usually don't include all the variables of interest in an economic model. This paper shows the identification of unobserved variables in observations at the population level. When the observables are distinct…

The design of a nonlinear Luenberger observer for a parametrized linear SISO (single-input single-output) system is studied. From an observability assumption of the system, the existence of such an observer is concluded. In a second step, a…

We develop a general theory of spatial solitons in a liquid crystalline medium exhibiting a nonlinearity with an arbitrary degree of effective nonlocality. The model accounts the observability of "accessible solitons" and establishes an…

This paper proposes a novel approach for designing functional observers for nonlinear systems, with linear error dynamics and assignable poles. Sufficient conditions for functional observability are first derived, leading to functional…

We introduce a novel parafermionic theory for which the conformal dimension of the basic parafermion is 3(1-1/k)/2, with k even. The structure constants and the central charges are obtained from mode-type associativity calculations. The…

When predicting scalar responses in the situation where the explanatory variables are functions, it is sometimes the case that some functional variables are related to responses linearly while other variables have more complicated…

Consider a scalar reflected diffusion $(X_t:t\geq 0)$, where the unknown drift function $b$ is modelled nonparametrically. We show that in the low frequency sampling case, when the sample consists of $(X_0,X_\Delta,...,X_{n\Delta})$ for…

Studying SLE$_{\kappa}$ on $S^2$ provides a new and interesting perspective for the conformality of some 2-dimensional physical models. We prove the existence and some basic properties of the spherical Minkowski content of SLE$_{\kappa}$,…

For the discrete series representations of ${\rm GL}(n)$ over a non-archimedean local field $F$, we define a notion of functions similar to "zonal spherical functions" for unramified principal series. We prove the existence of such…