Related papers: On symmetric one-dimensional diffusions

We investigate some analytic properties of traces of Dirichlet forms with respect to measures satisfying Hardy-type inequality. Among other results we prove convergence of spectra, ordered eigenvalues, eigenfunctions as well as convergence…

Given a symmetric Dirichlet form $(\mathcal{E},\mathcal{F})$ on a (non-trivial) $\sigma$-finite measure space $(E,\mathcal{B},m)$ with associated Markovian semigroup $\{T_{t}\}_{t\in(0,\infty)}$, we prove that $(\mathcal{E},\mathcal{F})$ is…

In this paper we study a certain regularity property of Axiom A flows over basic sets related to diameters of balls in Bowen's metric, which we call regular distortion along unstable manifolds. The motivation to investigate the latter comes…

What does the diffraction pattern from a single atom look like? How does it differ from the scattering from long range potential? With the development of new high-dynamic range pixel array detectors to measure the complete momentum…

The Dirichlet Laplacian in a curved three-dimensional tube built along a spatial (bounded or unbounded) curve is investigated in the limit when the uniform cross-section of the tube diminishes. Both deformations due to bending and twisting…

The properties of a particle diffusing on a one-dimensional lattice where at each site a random barrier and a random trap act simultaneously on the particle are investigated by numerical and analytical techniques. The combined effect of…

We consider discontinuous perturbations of smooth endomorphisms and show that if the perturbed family satisfies uniform mixing assumptions on standard pairs the physical measure is Lipschitz in the parameter defying the perturbation. We…

We study the branch of semi-stable and unstable solutions (i.e., those whose Morse index is at most one) of the Dirichlet boundary value problem $-\Delta u=\frac{\lambda f(x)}{(1-u)^2}$ on a bounded domain $\Omega \subset \R^N$, which…

We consider the distribution of a graph invariant of central similarity proximity catch digraphs (PCDs) based on one dimensional data. The central similarity PCDs are also a special type of parameterized random digraph family defined with…

We study in details the dynamics of the one dimensional symmetric trap model, via a real-space renormalization procedure which becomes exact in the limit of zero temperature. In this limit, the diffusion front in each sample consists in two…

In an earlier paper, we studied solutions g to convolution equations of the form a_d*g^{*d}+a_{d-1}*g^{*(d-1)}+...+a_1*g+a_0=0, where a_0, ..., a_d are given arithmetic functions associated with Dirichlet series which converge on some right…

The classical result by It\^o on the existence of strong solutions of stochastic differential equations (SDEs) with Lipschitz coefficients can be extended to the case where the drift is only measurable and bounded. These generalizations are…

We prove stability results for nonlinear diffusion equations of the porous medium and fast diffusion types with respect to the nonlinearity power $m$: solutions with fixed data converge in a suitable sense to the solution of the limit…

It is well-known under the name of `periodic homogenization' that, under a centering condition of the drift, a periodic diffusion process on R^d converges, under diffusive rescaling, to a d-dimensional Brownian motion. Existing proofs of…

We focus on a sequence of functions $\{f_n\}$, defined on a compact manifold with boundary $S$, converging in the $C^k$ metric to a limit $f$. A common assumption implicitly made in the empirical sciences is that when such functions…

Let $ \mathscr E $ be a regular, strongly local Dirichlet form on $L^2(X, m)$ and $d$ the associated intrinsic distance. Assume that the topology induced by $d$ coincides with the original topology on $ X$, and that $X$ is compact,…

A system of soft ellipsoid molecules confined between two planar walls is studied using classical Density Functional Theory (DFT). Both the isotropic and nematic phases are considered. The excess free energy is evaluated using two different…

Let $\mathbb{S} \subset \mathbb{C}$ be the circle in the plane, and let $\Omega: \mathbb{S} \to \mathbb{S}$ be an odd bi-Lipschitz map with constant $1+\delta_\Omega$, where $\delta_\Omega>0$ is small. Assume also that $\Omega$ is twice…

The aim of the paper is to address the behavior in large population of diffusions interacting on a random, possibly diluted and inhomogeneous graph. This is the natural continuation of a previous work, where the homogeneous Erd\H os-R\'enyi…

The investigation of the static and dynamic structural properties of colloidal systems relies on techniques capable of atomic resolution in real space and femtosecond resolution in time. Recently, the cross-correlation function (CCF)…