相关论文: Diffusing polygons and SLE($\kappa,\rho$)

Schramm-Loewner evolution (SLE$_\kappa$) is classically studied via Loewner evolution with half-plane capacity parametrization, driven by $\sqrt{\kappa}$ times Brownian motion. This yields a (half-plane) valued random field $\gamma = \gamma…

We obtain a stochastic differential equation (SDE) satisfied by the first $n$ coordinates of a Brownian motion on the unit sphere in $\mathbb{R}^{n+\ell}$. The SDE has non-Lipschitz coefficients but we are able to provide an analysis of…

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 study the diffusion of Brownian particles on the surface of a sphere and compute the distribution of solid angles enclosed by the diffusing particles. This function describes the distribution of geometric phases in two state quantum…

Polygonal slap maps are piecewise affine expanding maps of the interval obtained by projecting the sides of a polygon along their normals onto the perimeter of the polygon. These maps arise in the study of polygonal billiards with…

In this paper, we consider hypergeometric SLE process for $\kappa\in (4,8)$ and $\nu>\frac{\kappa}{2}-6$. Though the definition of hypergeometric SLE process is complicated, we show that given its hitting point on a specific boundary, its…

We introduce a new model called the Brownian Conga Line. It is a random curve evolving in time, generated when a particle performing a two dimensional Gaussian random walk leads a long chain of particles connected to each other by cohesive…

Our purpose in this paper is to determine the limiting distribution and the evolution rate of particles near the frontier of branching Brownian motions. Here the branching rate is given by a Kato class measure with compact support in…

This short note is motivated by a recently discovered connection between a drift-diffusion process in $n$-dimensional Euclidean space with a divergence-free drift sampled from a stationary and isotropic Gaussian ensemble of critical scaling…

This paper develops a fractional stochastic partial differential equation (SPDE) to model the evolution of a random tangent vector field on the unit sphere. The SPDE is governed by a fractional diffusion operator to model the L\'{e}vy-type…

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.

The analytical expressions for the time-dependent cross-correlations of the translational and rotational Brownian displacements of a particle with arbitrary shape are derived. The reference center is arbitrary, and the reference frame is…

Chordal SLE$_\kappa(\underline{\rho})$ is a natural variant of chordal SLE curve. It is a family of random non-crossing curves on the upper half plane from 0 to $\infty$, whose law is influenced by additional force points on $\mathbb R$.…

We use the interpretation of the Schramm-Loewner evolution as a limit of path measures tilted by a loop term in order to motivate the definition of $n$-radial SLE going to a particular point. In order to justify the definition we prove that…

In previous work [AHP24], we proved a finite-time large deviation principle in the Hausdorff metric for multiradial Schramm-Loewner evolution, SLE$(\kappa)$, as $\kappa \to 0$, with good rate function being the multiradial Loewner energy.…

In this article we obtain a skew-product decomposition of a Brownian motion on an ellipsoid of dimension $n$ in a Euclidean space of dimension $n+1$. We only consider such ellipsoid whose restriction to first $n$ dimensions is a sphere and…

We prove that, for $\kappa\le 4$, backward chordal SLE$_\kappa$ admits backward chordal SLE$_\kappa(-4,-4)$ decomposition for the capacity parametrization. This means that, for any bounded measurable subset $U\subset Q_4:={\mathbb…

This work is inspired by a remark of de Gennes about polyelectrolytes, which are charged polymers. A common model for a polymer is a self-avoiding or self-repelling random walk or Brownian motion. For polyelectrolytes, the repelling…

We construct an application, which takes as input a simple path and a possibly infinite collection of loops, and outputs a continuous path by adding the loops chronologically to the simple path as the simple path encounters them. By…

Recent theory and experiments have shown how the buildup of a high-concentration polymer layer at a one-dimensional solvent-air interface can lead to an evaporation rate that scales with time as $t^{-1/2}$ and that is insensitive to the…