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Related papers: Ergodicity of self-attracting motion

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We consider two types of non linear fast diffusion equations in R^N:(1) External drift type equation with general external potential. It is a natural extension of the harmonic potential case, which has been studied in many papers. In this…

Analysis of PDEs · Mathematics 2021-01-25 Chuqi Cao , Xingyu Li

We study the two-dimensional overdamped motion of an active particle whose orientational dynamics is subject to fractional Brownian noise, whereas its position is affected by self-propulsion and Brownian fluctuations. From a Langevin-like…

Statistical Mechanics · Physics 2020-07-21 Juan Ruben Gomez-Solano , Francisco J. Sevilla

Consider a d-dimensional Brownian motion in a random potential defined by attaching a nonnegative and polynomially decaying potential around Poisson points. We introduce a repulsive interaction between the Brownian path and the Poisson…

Probability · Mathematics 2013-10-04 Ryoki Fukushima

We briefly review the problem of Brownian motion and describe some intriguing facets. The problem is first treated in its original form as enunciated by Einstein, Langevin, and others. Then, utilizing the problem of Brownian motion as a…

Statistical Mechanics · Physics 2026-02-17 Sushanta Dattagupta , Aritra Ghosh

The hindered diffusion model is introduced. It is a continuum model giving the dynamics of a conserved density. Similar to the spin-facilitated models, the kinetics are hindered by a fluctuating diffusion coefficient that decreases as the…

Statistical Mechanics · Physics 2007-05-23 Gene F Mazenko

We investigate the ergodic properties of Brownian motion in heterogeneous media through the statistics of occupation times. Using the Feynman-Kac formalism, we derive analytical expressions for the distributions, moments, and ergodicity…

Statistical Mechanics · Physics 2025-11-17 Vicenç Méndez , Rosa Flaquer-Galmés

Bass and Pardoux (1987) deduce from the Krein-Rutman theorem a reverse ergodic theorem for a sub-probability transition function, which turns out to be a key tool in proving uniqueness of reflecting Brownian Motion in cones in Kwon and…

Probability · Mathematics 2024-08-15 Cristina Costantini , Thomas G. Kurtz

We studied the self-diffusion of colloidal ellipsoids in a monolayer near a flat wall by video microscopy. The image processing algorithm can track the positions and orientations of ellipsoids with sub-pixel resolution. The translational…

Soft Condensed Matter · Physics 2015-05-19 Zhongyu Zheng , Yilong Han

We study the asymptotic behavior of the maximum likelihood estimator corresponding to the observation of a trajectory of a Skew Brownian motion, through a uniform time discretization. We characterize the speed of convergence and the…

Probability · Mathematics 2015-03-17 Antoine Lejay , Ernesto Mordecki , Soledad Torres

In this article, we discuss ergodicity properties of a diffusion process given through an It\^{o} stochastic differential equation. We identify conditions on the drift and diffusion coefficients which result in sub-geometric ergodicity of…

Probability · Mathematics 2020-06-03 Petra Lazić , Nikola Sandrić

The microcanonical statistical mechanics of a set of self-gravitating particles is analyzed in mean-field approach. In order to deal with an upper bounded entropy functional, a softened gravitational potential is used. The softening is…

Statistical Mechanics · Physics 2008-11-26 Eduardo Follana , Victor Laliena

We study the asymptotic behaviour of a class of small-noise diffusions driven by fractional Brownian motion, with random starting points. Different scalings allow for different asymptotic properties of the process (small-time and tail…

Probability · Mathematics 2018-12-21 B. Horvath , A. Jacquier , C. Lacombe

A succesful method to describe the asymptotic behavior of a discrete time stochastic process governed by some recursive formula is to relate it to the limit sets of a well chosen mean differential equation. Under an attainability condition,…

Probability · Mathematics 2011-01-19 Mathieu Faure , Gregory Roth

We analyze quantal Brownian motion in $d$ dimensions using the unified model for diffusion localization and dissipation, and Feynman-Vernon formalism. At high temperatures the propagator possess a Markovian property and we can write down an…

Condensed Matter · Physics 2009-10-31 Doron Cohen

In this paper we provide convergence analysis for a class of Brownian queues in tandem by establishing an exponential drift condition. A consequence is the uniform exponential ergodicity for these multidimensional diffusions, including the…

Probability · Mathematics 2019-06-18 Wenpin Tang

This paper concerns the so-called diffusion in the curl of the 2d Gaussian free field, and its generalization to higher dimensions $n \geq 2$, building on the scale-by-scale homogenization approach developed recently by Chatzigeorgiou,…

Probability · Mathematics 2025-11-20 Peter S. Morfe , Felix Otto , Christian Wagner

We have proposed a method for the dynamic simulation of a collection of self-propelled particles in a viscous Newtonian fluid. We restrict attention to particles whose size and velocity are small enough that the fluid motion is in the…

Soft Condensed Matter · Physics 2015-05-13 Vishwajeet Mehandia , Prabhu R. Nott

Motivated by the simple models of molecular motor obeying a linear force-velocity relation, we have studied the stochastic dynamics of a Brownian particle in the presence of a linear velocity dependent force, $f_s(1-\frac{v}{v_0})$ where…

Statistical Mechanics · Physics 2021-08-19 Arsha N , Shabina S , Mamata Sahoo

We study general aspects of active motion with fluctuations in the speed and the direction of motion in two dimensions. We consider the case in which fluctuations in the speed are not correlated to fluctuations in the direction of motion,…

Biological Physics · Physics 2009-11-13 Fernando Peruani , Luis G. Morelli

The main results in this paper concern large and moderate deviations for the radial component of a $n$-dimensional hyperbolic Brownian motion (for $n\geq 2$) on the Poincar\'{e} half-space. We also investigate the asymptotic behavior of the…

Probability · Mathematics 2018-01-09 Valentina Cammarota , Alessandro De Gregorio , Claudio Macci