Related papers: Reversed radial SLE and the Brownian loop measure
We show the linear drift of the Brownian motion on the universal cover of a closed connected Riemannian manifold is $C^{k-2}$ differentiable along any $C^{k}$ curve in the manifold of $C^k$ metrics with negative sectional curvature. We also…
We consider the model of the Brownian plane, which is a pointed non-compact random metric space with the topology of the complex plane. The Brownian plane can be obtained as the scaling limit in distribution of the uniform infinite planar…
We numerically show that the statistical properties of the shortest path on critical percolation clusters are consistent with the ones predicted for Schramm-Loewner evolution (SLE) curves for $\kappa=1.04\pm0.02$. The shortest path results…
We revisit the Bieberbach conjecture in the framework of SLE processes and, more generally, L\'evy processes. The study of their unbounded whole-plane versions leads to a discrete series of exact results for the expectations of coefficients…
We derive a rate of convergence of the Loewner driving function for planar loop-erased random walk to Brownian motion with speed 2 on the unit circle, the Loewner driving function for radial SLE(2). The proof uses a new estimate of the…
We introduce a natural "massive" version of the Brownian loop soup of Lawler and Werner which displays conformal covariance and exponential decay. We show that this massive Brownian loop soup arises as the near-critical scaling limit of a…
In this article, the structure of semiclassical measures for solutions to the linear Schr\"{o}dinger equation on the torus is analysed. We show that the disintegration of such a measure on every invariant lagrangian torus is absolutely…
In 2003 Lawler and Werner introduced the Brownian loop measure and studied some of its properties. Cardy and Gamsa has predicted a formula for the total mass of the Brownian loop measure on the set of simple loops in the upper half plane…
Given a planar domain $D$, the harmonic measure distribution function $h_D(r)$, with base point $z$, is the harmonic measure with pole at $z$ of the parts of the boundary which are within a distance $r$ of $z$. Equivalently it is the…
The standard kinetic path integral for all spatially closed Brownian paths (loops) of duration t weighted by the product mn is evaluated, where m and n are the linking numbers of the Brownian loop with two arbitrary curves in 3D space. The…
The development of superresolution techniques, i.e., allowing for efficient resolution below the Rayleigh limit, became one of the important branches in contemporary optics and metrology. Recent findings show that perfect spatial mode…
The Brownian sphere is a random metric space, homeomorphic to the two-dimensional sphere, which arises as the universal scaling limit of many types of random planar maps. The direct construction of the Brownian sphere is via a continuous…
In this paper, we propose to study spectral measures on local fields. Some basic results are presented, including the stability of Bessel sequences under perturbation, the Landau theorem on Beurling density, the law of pure type of spectral…
In this paper we explore the connection between quantitative rectifiability of measures and the $L^2$ boundedness of the codimension one Riesz transform. Among other things, we prove the following. Let $\mu$ be a Radon measure in $\mathbb…
We discuss the extension of radial SLE to multiply connected planar domains. First, we extend Loewner's theory of slit mappings to multiply connected domains by establishing the radial Komatu-Loewner equation, and show that a simple curve…
It is known that a backward Schramm--Loewner evolution (SLE) is coupled with a free boundary Gaussian free field (GFF) with boundary perturbation to give conformal welding of quantum surfaces. Motivated by a generalization of conformal…
Let $G/K$ be a Riemannian symmetric space of noncompact type, and let $\nu_{a_j}$, $j=1,...,r$ be some orbital measures on $G$ (see the definition below). The aim of this paper is to study the $L^{2}$-regularity (resp. $C^k$-smoothness) of…
The stochastic rotational invariance of an integration by parts formula inspired by the Bismut approach to Malliavin calculus is proved in the framework of the Lie symmetry theory of stochastic differential equations. The non-trivial effect…
We construct a class of iterated stochastic integrals with respect to Brownian motion on an abstract Wiener space which allows for the definition of Brownian motions on a general class of infinite-dimensional nilpotent Lie groups based on…
The development of a mechanics of non-differentiable paths suggested by Scale Relativity results in a foundation of Quantum Mechanics including Schr\"odinger's equation and all the other axioms under the assumption the path…