Related papers: Multiple-paths $SLE_\kappa$ in multiply connected …

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…

Let $\rm{Bun}$ be the moduli stack of rank $2$ bundles with fixed determinant on a smooth proper curve $C$ over a local field $F$. We show how to associate with a Schwartz $\kappa$-density, for $\rm{Re}(\kappa)\ge 1/2$, a smooth function on…

Levy-Loewner evolution (LLE) is a generalization of the Schramm-Loewner evolution (SLE) where the branching is possible in a course of growth process. We consider a class of radial Levy-Loewner evolutions for which sets of points of the…

We define intermediate SLE$_\kappa(\underline\rho)$ and reversed intermediate SLE$_\kappa(\underline\rho)$ processes using Appell-Lauricella multiple hypergeometric functions, and use them to describe the time-reversal of…

We study the scaling limit of planar loop erased random walk (LERW) on the percolation cluster, with occupation probability $p\geq p_c$. We numerically demonstrate that the scaling limit of planar LERW$_p$ curves, for all $p>p_c$, can be…

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…

If kappa is strongly compact, lambda > kappa is regular, then (2^{< lambda})^+ --> (lambda+eta)^2_theta holds for eta,theta<kappa.

The Schramm-Loewner evolution (SLE) is a powerful tool to describe fractal interfaces in 2D critical statistical systems. Yet the application of SLE is well established for statistical systems described by quantum field theories satisfying…

SLE$_{\kappa}(\rho)$ is a variant of SLE$_{\kappa}$ where $\rho$ characterizes the repulsion (if $\rho>0$) or attraction $(\rho<0)$ from the boundary. This paper examines the probabilities of SLE$_{\kappa}(\rho)$ to get close to the…

We consider multiple radial SLE as the number of curves tends to infinity. We give conditions that imply the tightness of the associated processes given by the Loewner equation. In the case of equal weights, the infinite-slit limit is…

We prove a strong large deviation principle (LDP) for multiple chordal SLE$_{0+}$ curves with respect to the Hausdorff metric. In the single-chord case, this result strengthens an earlier partial result by the second author. We also…

Let $\kappa \in \mathbb{N}_+^\ell$ satisfy $\kappa_1 + \dots + \kappa_\ell = n$ and let $\mathcal{U}_\kappa$ denote the "multislice" of all strings $u$ in $[\ell]^n$ having exactly $\kappa_i$ coordinates equal to $i$, for all $i \in…

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 numerically test the correspondence between the scaling limit of self-avoiding walks (SAW) in the plane and Schramm-Loewner evolution (SLE) with k=8/3. We introduce a discrete-time process approximating SLE in the exterior of the unit…

We consider bipolar oriented random planar maps with heavy-tailed face degrees. We show for each $\alpha \in (1,2)$ that if the face degree is in the domain of attraction of an $\alpha$-stable L\'evy process, the corresponding random planar…

We develop a general theory of multiple chordal $\mathrm{SLE}(0)$ systems of type $(n, m)$ for positive integers $n$ and $m$ with $m \leq \lfloor n/2 \rfloor$, extending the construction of~\cite{ABKM20} beyond the previously studied case…

Schramm Loewner Evolutions (SLE) are random increasing hulls defined through the Loewner equation driven by Brownian motion. It is known that the increasing hulls are generated by continuous curves. When the driving process is of the form…

A new method to study a stopped hull of SLE(kappa,rho) is presented. In this approach, the law of the conformal map associated to the hull is invariant under a SLE induced flow. The full trace of a chordal SLE(kappa) can be studied using…

An annulus SLE$_\kappa$ trace tends to a single point on the target circle, and the density function of the end point satisfies some differential equation. Some martingales or local martingales are found for annulus SLE$_4$, SLE$_8$ and…

This article focuses on the characterization of global multiple Schramm-Loewner evolutions (SLE). The chordal SLE describes the scaling limit of a single interface in various critical lattice models with Dobrushin boundary conditions, and…