相关论文: Loewner Chains

Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems is crucial in many scientific and engineering domains such as fluid dynamics, weather forecasting and their inverse optimization problems.…

The recently introduced SLE growth processes are based on conformal maps from an open and simply-connected subset of the upper half-plane to the half-plane itself. We generalize this by considering a hierarchy of stochastic evolutions…

Graphs are a widely used paradigm for representing non-Euclidean data, with applications ranging from social network analysis to biomolecular prediction. While graph learning has achieved remarkable progress, real-world graph data presents…

Positional and relational perspectives on network data have led to two different research traditions in textual analysis and social network analysis, respectively. Latent Semantic Analysis (LSA) focuses on the latent dimensions in textual…

Interfaces in a model with a single, real nonconserved order parameter and purely dissipative evolution equation are considered. We show that a systematic perturbative approach, called the expansion in width and developed for curved domain…

We discuss the partition function point of view for chordal Schramm-Loewner evolutions and their relationship with correlation functions in conformal field theory. Both are closely related to crossing probabilities and interfaces in…

Let R be a hyperbolic Riemann surface with boundary $\partial R$ and suppose that $\gamma:[0,T]\to R\cup\partial R$ is a simple curve growing from the boundary of R. By lifting $R_{t}=R\setminus \gamma(0,t]$ to the universal covering space…

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…

Schramm Loewner Evolution (SLE) is a one-parameter family of random planar curves introduced by Oded Schramm in 1999 as the candidates for the scaling limits of the interfaces in the planar critical lattice models. This is the only possible…

Substantial progress has been made in recent years on the 2D critical percolation scaling limit and its conformal invariance properties. In particular, chordal SLE6 (the Stochastic Loewner Evolution with parameter k=6) was, in the work of…

Variational problems of splitting-type with mixed linear-superlinear growth conditions are considered. In the twodimensional case the minimizing problem is given by \[ J [w] = \int_{\Omega} \Big[f_1\big(\partial_1 w\big) +…

Description of evolution between spatial slices in a general spacetime suffers from a significant difficulty: the states on the slices, in a given basis, are not related by a unitary transformation. This problem, which occurs in spacetime…

The paper suggests a generalisation of the diffusion-limited aggregation (DLA) based on using a general stochastic process to control particle movements before sticking to a growing cluster. This leads to models with variable…

The dynamics of a one dimensional growth model involving attachment and detachment of particles is studied in the presence of a localized growth inhomogeneity along with anchored boundary conditions. At large times, the latter enforce an…

In a recent work [Phys. Rev. E 109, L042102 (2024)], interesting dimensional crossovers [from two- to one-dimensional (2D to 1D) scaling] were found in the growth of Kardar-Parisi-Zhang (KPZ) interfaces on rectangular substrates, with…

This article presents a new mathematical framework to perform statistical analysis on time-indexed sequences of 2D or 3D shapes. At the core of this statistical analysis is the task of time interpolation of such data. Current models in use…

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…

A nested family of growing or shrinking planar domains is called a Laplacian growth process if the normal velocity of each domain's boundary is proportional to the gradient of the domain's Green function with a fixed singularity on the…

Emerging applications of machine learning in numerous areas involve continuous gathering of and learning from streams of data. Real-time incorporation of streaming data into the learned models is essential for improved inference in these…

Networks with a prescribed power-law scaling in the spectrum of the graph Laplacian can be generated by evolutionary optimization. The Laplacian spectrum encodes the dynamical behavior of many important processes. Here, the networks are…