Related papers: Multiple SLEs and Dyson Brownian motion: transitio…
We review two numerical methods related to the Schramm-Loewner evolution (SLE). The first simulates SLE itself. More generally, it finds the curve in the half-plane that results from the Loewner equation for a given driving function. The…
Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process, including Fractional Brownian motion. The purpose is the comparison with a deterministic PDE, which in certain…
SLE is a random growth process based on Loewner's equation with driving parameter a one-dimensional Brownian motion running with speed $\kappa$. This process is intimately connected with scaling limits of percolation clusters and with the…
Brownian dynamics simulations of bidisperse hard discs moving in two dimensions in a given steady and homogeneous shear flow are presented close to and above the glasstransition density. The stationary structure functions and stresses of…
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.
The Dyson Brownian motion model for transistions to the CUE is considered. For initial eigenvalue probability density functions corresponding to the COE and CSE, the density-density correlation function between an eigenvalue at position…
We relate the formulas giving Brownian (and other) intersection exponents to the absolute continuity relations between Bessel process of different dimensions, via the two-parameter family of Schramm-Loewner Evolution processes…
By incorporating the proper boundary conditions, we analytically derive the impulse response (or "Green's function") of a current-sensing spin detector. We also compare this result to a Monte-Carlo simulation (which automatically takes the…
We study the Loewner evolution whose driving function is $W_t = B_t^1 + i B_t^2$, where $(B^1,B^2)$ is a pair of Brownian motions with a given covariance matrix. This model can be thought of as a generalization of Schramm-Loewner evolution…
In this paper, we prove a sufficient and necessary condition for the transition probability distribution of a general, time-inhomogeneous linear SDE to possess a density function and study the differentiability of the density function and…
The paper is devoted to the multiple chordal Loewner differential equation with different driving functions on two time intervals. We obtain exact implicit or explicit solutions to the Loewner equations with piecewise constant driving…
Schramm-Loewner Evolutions ($\SLE$) are random curves in planar simply connected domains; the massless (Euclidean) free field in such a domain is a random distribution. Both have conformal invariance properties in law. In the present…
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 (SLEs) have proved an efficient way to describe a single continuous random conformally invariant interface in a simply-connected planar domain; the admissible probability distributions are parameterized by a…
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 investigate coherent transport through open lateral quantum dots using recursive Green's function technique, incorporating exchange-correlation effects within local spin-density approximation (LSDA). At low electron densities the current…
We study the probabilities with which chordal Schramm-Loewner Evolutions (SLE) visit small neighborhoods of boundary points. We find formulas for general chordal SLE boundary visiting probability amplitudes, also known as SLE boundary…
Keldysh nonequilibrium Green's function method is utilized to study theoretically the spin polarized transport through a graphene spin valve irradiated by a monochromatic laser field. It is found that the bias dependence of the differential…
This article provides an introduction to Schramm(stochastic)-Loewner evolution (SLE) and to its connection with conformal field theory, from the point of view of its application to two-dimensional critical behaviour. The emphasis is on the…
SLE(kappa,rho) is a generalisation of Schramm-Loewner evolution which describes planar curves which are statistically self-similar but not conformally invariant in the strict sense. We show that, in the context of boundary conformal field…