Related papers: The configurational measure on mutually avoiding S…
We develop an approach for performing scaling analysis of $N$-step Random Walks (RWs). The mean square end-to-end distance, $\langle\vec{R}_{N}^{2}\rangle$, is written in terms of inner persistence lengths (IPLs), which we define by the…
Standard stochastic Loewner evolution (SLE) is driven by a continuous Brownian motion, which then produces a continuous fractal trace. If jumps are added to the driving function, the trace branches. We consider a generalized SLE driven by a…
The Brownian loop measure is a conformally invariant measure on loops in the plane that arises when studying the Schramm-Loewner evolution (SLE). When an SLE curve in a domain evolves from an interior point, it is natural to consider the…
We suggest an approximate method of finding a conformal mapping of an annulus onto an arbitrary bounded doubly connected polygonal domain. The method is based on the parametric Loewner--Komatu method. We consider smooth one parameter…
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…
The level lines of the Gaussian free field are known to be related to SLE(4). It is shown how this relation allows to define chordal SLE(4) processes on doubly connected domains, describing traces that are anchored on one of the two…
The (chordal) Loewner differential equation encodes certain curves in the half-plane (aka traces) by continuous real-valued driving functions. Not all curves are traces; the latter can be defined via a geometric condition called the local…
Two-dimensional loop-erased random walks (LERWs) are random planar curves whose scaling limit is known to be a Schramm-Loewner evolution SLE_k with parameter k = 2. In this note, some properties of an SLE_k trace on doubly-connected domains…
This article is meant to serve as a guide to recent developments in the study of the scaling limit of critical models. These new developments were made possible through the definition of the Stochastic Loewner Evolution (SLE) by Oded…
In order to characterize molecular structures we introduce configurational fingerprint vectors which are counterparts of quantities used experimentally to identify structures. The Euclidean distance between the configurational fingerprint…
We review some of the results related to conformal restriction: the chordal case and the radial case. We describe Brownian intersection exponents, conformal restriction property and SLE, and study their properties.
When studying stochastic processes, it is often fruitful to have an understanding of several different notions of regularity. One such notion is the optimal H\"older exponent obtainable under reparametrization. In this paper, we show that…
We consider random conformally invariant paths in the complex plane (SLEs). Using the Coulomb gas method in conformal field theory, we rederive the mixed multifractal exponents associated with both the harmonic measure and winding (rotation…
We present a way to study the conformal structure of random planar maps. The main idea is to explore the map along an SLE (Schramm--Loewner evolution) process of parameter $ \kappa = 6$ and to combine the locality property of the SLE_{6}…
Schramm-Loewner Evolution (SLE) is a stochastic process that helps classify critical statistical models using one real parameter $\kappa$. Numerical study of SLE often involves curves that start and end on the real axis. To reduce numerical…
We define a class of random measures, spatially independent martingales, which we view as a natural generalisation of the canonical random discrete set, and which includes as special cases many variants of fractal percolation and Poissonian…
Empirical research in many social disciplines involves constructs that are not directly observable, such as behaviors. To model them, constructs must be operationalized using their relations with indicators. Structural equation modeling…
The paper analyzes a specific class of random walks on quotients of $X:=\text{SL}(k,{\Bbb R})/ \Gamma$ for a lattice $\Gamma$. Consider a one parameter diagonal subgroup, $\{g_t\}$, with an associated abelian expanding horosphere, $U\cong…
It was argued by Schramm and Smirnov that the critical site percolation exploration path on the triangular lattice converges in distribution to the trace of chordal SLE(6). We provide here a detailed proof, which relies on Smirnov's theorem…
We consider multiple radial SLE curves with various time parameterizations and possible spiraling behavior. We construct them by tilting independent radial SLEs with a suitable local martingale, generalizing the earlier construction by…