Related papers: From CLE(\kappa) to SLE(\kappa,\rho)'s

Libraries of Low-Rank Adaptation (LoRA) adapters are becoming a practical by-product of parameter-efficient adaptation. Once such adapters accumulate, a natural question is no longer how to train one adapter for one task, but how to reuse…

We derive boundary arm exponents for SLE. Combining with the convergence of critical lattice models to SLE, these exponents would give the alternating half-plane arm exponents for the corresponding lattice models.

We introduce partially observable concurrent Kleene algebra (POCKA), an algebraic framework to reason about concurrent programs with control structures, such as conditionals and loops. POCKA enables reasoning about programs that can access…

This article pertains to the classification of multiple Schramm-Loewner evolutions (SLE). We construct the pure partition functions of multiple SLE$(\kappa)$ with $\kappa \in (0,4]$ and relate them to certain extremal multiple SLE measures,…

We construct the canonical geodesic metric on the gasket of conformal loop ensembles (CLE$_\kappa$) in the regime $\kappa \in (4,8)$ where the loops intersect themselves, each other, and the domain boundary. Previous work of the authors and…

Stochastic Loewner Evolutions (SLE) with a multiple sqrt(kappa)B of Brownian motion B as driving process are random planar curves (if kappa<=4) or growing compact sets generated by a curve (if kappa>4). We consider here more general Levy…

We derive boundary arm exponents and interior arm exponents for SLE$(\kappa)$. Combining with the possible convergence of critical lattice models to SLE, these exponents would give the corresponding alternating half-plane arm exponents and…

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…

We build models using an indiscernible model sub-structures of ${\kappa} \ge {\lambda}$ and related more complicated structures. We use this to build various Boolean algebras.

A space of local martingales of SLE type growth processes forms a representation of Virasoro algebra, but apart from a few simplest cases not much is known about this representation. The purpose of this article is to exhibit examples of…

For random collections of self-avoiding loops in two-dimensional domains, we define a simple and natural conformal restriction property that is conjecturally satisfied by the scaling limits of interfaces in models from statistical physics.…

In this paper we consider the natural random walk on a planar graph and scale it by a small positive number $\delta$. Given a simply connected domain $D$ and its two boundary points $a$ and $b$, we start the scaled walk at a vertex of the…

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).…

We consider the Schramm-Loewner evolution (SLE$_\kappa$) for $\kappa \in (4,8)$, which is the regime that the curve is self-intersecting but not space-filling. We let ${\mathcal K}$ be the set of $\kappa \in (4,8)$ for which the adjacency…

We find explicit formulas for the probabilities of general boundary visit events for planar loop-erased random walks, as well as connectivity events for branches in the uniform spanning tree. We show that both probabilities, when suitably…

The aim of these notes is threefold. First, we discuss geometrical aspects of conformal covariance in stochastic Schramm-Loewner evolutions (SLEs). This leads us to introduce new ``dipolar'' SLEs, besides the known chordal, radial or…

We present an elementary proof establishing the equality of the right and left-sided $\sqrt{\kappa}$-quantum lengths for an SLE$_\kappa$ curve, where $\kappa\in (0,4]$. We achieve this by demonstrating that the$\sqrt{\kappa}$-quantum length…

This paper introduces the annulus SLE$_\kappa$ processes in doubly connected domains. Annulus SLE$_6$ has the same law as stopped radial SLE$_6$, up to a time-change. For $\kappa\not=6$, some weak equivalence relation exists between annulus…

We give a simplified and complete proof of the convergence of the chordal exploration process in critical FK-Ising percolation to chordal SLE$_\kappa( \kappa-6)$ with $\kappa=16/3$. Our proof follows the classical excursion-construction of…

We consider chordal SLE(kappa) curves for kappa > 4, where the intersection of the curve with the boundary is a random fractal of almost sure Hausdorff dimension min {2-8/kappa,1}. We study the random sets of points at which the curve…