Related papers: On the smoothness of the partition function for mu…
We have studied the iso-height lines on the $\mathrm{WO_3}$ surface as a physical candidate for conformally invariant curves. We have shown that these lines are conformally invariant with the same statistics of domain walls in the critical…
We study the relationship between certain SLE$_\kappa(\rho)$ processes, which are variants of the Schramm-Loewner evolution with parameter $\kappa$ in which one keeps track of an extra marked point, and Liouville quantum gravity (LQG).…
Conformally-invariant curves that appear at critical points in two-dimensional statistical mechanics systems, and their fractal geometry have received a lot of attention in recent years. On the one hand, Schramm has invented a new rigorous…
We develop a theory for the multiple radial $\mathrm{SLE}(\kappa)$ systems with parameter $\kappa > 0$ -- a family of random multi-curve systems in a simply connected domain $\Omega$, with marked boundary points $z_1, \ldots, z_n \in…
Motivated by string theory connection, a covariant procedure for perturbative calculation of the partition function of the two-dimensional generalized $\sigma$-model is considered. The importance of a consistent regularization of the…
In this article, we study multiple $SLE_\kappa$, for $\kappa\in(0,4]$, driven by Dyson Brownian motion. This model was introduced in the unit disk by Cardy in connection with the Calogero-Sutherland model. We prove the Carath\'eodory…
We make use of the fact that a two-sided whole-plane Schramm-Loewner evolution (SLE$_\kappa$) curve $\gamma$ for $\kappa\in(0,8)$ from $\infty$ to $\infty$ through $0$ may be parametrized by its $d$-dimensional Minkowski content, where…
Using the estimate of the difference between the discrete harmonic function and its corresponding continuous version we derive a rate of convergence of the Loewner driving function for the harmonic explorer to the Brownian motion with speed…
In this paper, we discuss the chordal Komatu-Loewner equation on standard slit domains in a manner applicable not just to a simple curve but also a family of continuously growing hulls. Especially a conformally invariant characterization of…
We prove that the chordal SLE$_\kappa$ trace is reversible for $\kappa\in(0,4]$.
We have numerically studied the properties of the interface induced in the ferromagnetic random-bond three-state Potts model by symmetry-breaking boundary conditions. The fractal dimension $d_f$ of the interface was determined. The…
We investigate the relation between the Laplacian-$b$ motion and stochastic Komatu-Loewner evolution (SKLE) on multiply connected subdomains of the upper half-plane, both of which are analogues to SLE. In particular, we show that, if the…
The Stochastic Loewner equation, introduced by Schramm, gives us a powerful way to study and classify critical random curves and interfaces in two-dimensional statistical mechanics. New kind of stochastic Loewner equation, called fractional…
Stochastic Loewner evolution also called Schramm Loewner evolution (abbreviated, SLE) is a rigorous tool in mathematics and statistical physics for generating and studying scale invariant or fractal random curves in two dimensions. The…
We give a new, short computation of pairing probabilities for multiple chordal interfaces in the critical Ising model, the harmonic explorer, and for multiple level lines of the Gaussian free field. The core of the argument are the known…
We prove that the chordal SLE$_{\kappa}$ trace is reversible for $\kappa\in(0,4]$.
Schramm-Loewner evolution appears as the scaling limit of interfaces in lattice models at critical point. Critical behavior of these models can be described by minimal models of conformal field theory. Certain CFT correlation functions are…
We first prove that, for $\kappa\in(0,4)$, a whole-plane SLE$(\kappa;\kappa+2)$ trace stopped at a fixed capacity time satisfies reversibility. We then use this reversibility result to prove that, for $\kappa\in(0,4)$, a chordal…
Given a partition $\lambda$, we write $e_j(\lambda)$ for the $j^{\textrm{th}}$ elementary symmetric polynomial $e_j$ evaluated at the parts of $\lambda$ and $e_jp_A(n)$ for the sum of $e_j(\lambda)$ as $\lambda$ ranges over the set of…
Let $\nabla^\lambda$ denote the Schur functor labelled by the partition $\lambda$ and let $E$ be the natural representation of $\mathrm{SL}_2(\mathbb{C})$. We make a systematic study of when there is an isomorphism $\nabla^\lambda…