Related papers: The Brownian Map
We study a model for the entanglement of a two-dimensional reflecting Brownian motion in a bounded region divided into two halves by a wall with three or more small windows. We map the Brownian motion into a Markov Chain on the fundamental…
A map is an abstract visual representation of a region, taken from a given space, usually designed for final human consumption. Traditional cartography focuses on the mapping of Euclidean spaces by using some distance metric. In this paper…
This article contains both a point process and a sequential description of the greatest convex minorant of Brownian motion on a finite interval. We use these descriptions to provide new analysis of various features of the convex minorant…
We consider functional equations (Cauchy's, Abel's and some other functional equations) and show that to find general solution of these equations is equivalent to establish that a space-transformation of a Brownian Motion by suitable…
We state an exact simulation scheme for the first passage time of a Brownian motion to a symmetric linear boundary.
Quantum brownian motion is a fundamental model for a proper understanding of open quantum systems in different contexts such as chemistry, condensed matter physics, bio-physics and opto- mechamics. In this paper we propose a novel approach…
Brownian motion provides a bedrock for the understanding of soft condensed matter and, therefore, of the physical description of the microscopic biological world. Inspired by this domain, and combining softness with hydrodynamic energy…
Brownian motion is the perpetual irregular motion exhibited by small particles immersed in a fluid. Such random motion of the particles is produced by statistical fluctuations in the collisions they suffer with the molecules of the…
We define what we call an on/off Brownian snake. We use this to construct on/off super Brownian motion recently introduced to the literature by Blath and Jacobi and which is a measure-valued branching process with a dormant state and an…
Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the…
For the standard map the homotopically non-trivial invariant curves of rotation number satisfying the Bryuno condition are shown to be analytic in the perturbative parameter, provided the latter is small enough. The radius of convergence of…
We consider the area of spheres centered at the distinguished point in the Brownian plane. As a function of the radius, the resulting process has continuously differentiable sample paths. Furthermore, the pair consisting of the process and…
A graduate level textbook on the interplay between complex analysis and Brownian motion.
The invariance properties of Brownian motion are investigated and revisited within a recent Lie symmetry approach to stochastic differential equations. Some notable properties of the process can be recovered by a related integration by…
The bijectivity of the mapping, which is represented as expectation, from a family of Gaussian measures parametrized by linear combinations of Dirac measures to the space of classical reflectionless potentials is shown. It is also shown…
The Brownian web (BW) is the random network formally consisting of the paths of coalescing one-dimensional Brownian motions starting from every space-time point in R\timesR. We extend the earlier work of Arratia and of Toth and Werner by…
A classical model of Brownian motion consists of a heavy molecule submerged into a gas of light atoms in a closed container. In this work we study a 2D version of this model, where the molecule is a heavy disk of mass M and the gas is…
The conformal dimension of a metric space $(X, d)$ is equal to the infimum of the Hausdorff dimensions among all metric spaces quasisymmetric to $(X, d)$. It is an important quasisymmetric invariant which lies non-strictly between the…
In this paper, we introduce some known map projections from a model of the Earth to a flat sheet of paper or map and derive the plotting equations for these projections. The first fundamental form and the Gaussian fundamental quantities are…
Classical objectivity as a property of quantum states---a view proposed to explain the observer-independent character of our world from quantum theory, is an important step in bridging the quantum-classical gap. It was recently derived in…