Related papers: Loewner chains and evolution families on parallel …

We suggest how to give a physical interpretation of Stochastic Loewner Evolution traces approaching a marked point in the upper half plane. We show that this may be related to the fusion of boundary with bulk fields in Conformal Field…

One-parameter semigroups of holomorphic functions appear naturally in various applications of Complex Analysis, and in particular, in the theory of (temporally) homogeneous Markov processes. A suitable analogue of one-parameter semigroups…

A class of oscillating Lorentz covariant configurations for the evolution of the domain walls in diverse dimensions are analytically obtained. It is shown that the oscillating solutions in the case of domain walls are responsible for…

We prove that any disjoint union of finitely many simple curves in the upper half-plane can be generated in a unique way by the chordal multiple-slit Loewner equation with constant weights.

In this paper we introduce a general version of the Loewner differential equation which allows us to present a new and unified treatment of both the radial equation introduced in 1923 by K. Loewner and the chordal equation introduced in…

The one-dimensional chain of coupled oscillators with long-range power-law interaction is considered. The equation of motion in the infrared limit are mapped onto the continuum equation with the Riesz fractional derivative of order…

In 1972, Becker [J. Reine Angew. Math. 255 (1972), 23-43] discovered a construction of quasiconformal extensions making use of the classical radial Loewner chains. In this paper we develop a chordal analogue of Becker's construction. As an…

The paper develops the Loewner approach for data-based modeling of a linear distributed-parameter system. This approach is applied to a controlled flexible beam model coupled with a spring-mass system. The original dynamical system is…

We define the Schramm-Loewner evolution (SLE) in multiply connected domains for kappa \leq 4 using the Brownian loop measure. We show that in the case of the annulus, this is the same measure obtained recently by Dapeng Zhan. We use the…

Building on H. Tran's study of Loewner hulls generated by complex-valued driving functions, which showed the existence of a phase transition, we answer the question of whether the phase transition for complex-driven hulls matches the phase…

We provide multiple Schramm-Loewner evolutions (SLEs) to describe the scaling limit of multiple interfaces in critical lattice models possessing Lie algebra symmetries. The critical behavior of the models is described by Wess-Zumino-Witten…

The classical Loewner's theorem states that operator monotone functions on real intervals are described by holomorphic functions on the upper half-plane. We characterize local order isomorphisms on operator domains by biholomorphic…

Let $D={\mathbb H}\setminus \bigcup_{j=1}^N C_j$ be a standard slit domain, where ${\mathbb H}$ is the upper half plane and $C_j,1\le j\le N,$ are mutually disjoint horizontal line segments in ${\mathbb H}$. A stochastic Komatu-Loewner…

We discuss the possible candidates for conformally invariant random non-self-crossing curves which begin and end on the boundary of a multiply connected planar domain, and which satisfy a Markovian-type property. We consider both, the case…

We present an algorithm, based on the iteration of conformal maps, that produces independent samples of self-avoiding paths in the plane. It is a discrete process approximating radial Schramm-Loewner evolution growing to infinity. We focus…

This paper studies the behavior of solutions near the explosion time to the chordal Komatu-Loewner equation for slits, motivated by the preceding studies by Bauer and Friedrich (2008) and by Chen and Fukushima (2018). The solution to this…

This work brings together the moment matching approach based on Loewner functions and the classical Loewner framework based on the Loewner pencil in the case of bilinear systems. New Loewner functions are defined based on the bilinear…

We consider evolution in the unit disk in which the sample paths are represented by the trajectories of points evolving randomly under the generalized Loewner equation. The driving mechanism differs from the SLE evolution, but nevertheless…

In this contribution, we discuss the modeling and model reduction framework known as the Loewner framework. This is a data-driven approach, applicable to large-scale systems, which was originally developed for applications to linear…

We analyse the so-called small-world network model (originally devised by Strogatz and Watts), treating it, among other things, as a case study of non-linear coupled difference or differential equations. We derive a system of evolution…