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Related papers: Large deviations and a Kramers' type law for self-…

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We numerically investigate the mean exit time of an inertial active Brownian particle from a circular cavity with single or multiple exit windows. Our simulation results witness distinct escape mechanisms depending upon the relative…

Statistical Mechanics · Physics 2025-08-18 Tanwi Debnath , Pinaki Chaudhury , Taritra Mukherjee , Debasish Mondal , Pulak K. Ghosh

In this paper we study the fluctuations from the limiting behavior of small noise random perturbations of diffusions with multiple scales. The result is then applied to the exit problem for multiscale diffusions, deriving the limiting law…

Probability · Mathematics 2015-02-20 Sergio A. Almada Monter , Konatantinos Spiliopoulos

We study the trajectories followed by a particle subjected to weak noise when escaping from the domain of attraction of a stable fixed point. If detailed balance is absent, a _focus_ may occur along the most probable exit path, leading to a…

chao-dyn · Physics 2008-02-03 Robert S. Maier , Daniel L. Stein

We derive a large deviation principle for families of random variables in the basin of attraction of spectrally positive stable distributions by proving a uniform version of the Tauberian theorem for Laplace-Stieltjes transforms. The main…

Probability · Mathematics 2026-05-25 Giampaolo Cristadoro , Gaia Pozzoli

We study a Schilder-type large deviation principle for sticky-reflected Brownian motion with boundary diffusion, both at the static and sample path level in the short-time limit. A sharp transition for the rate function occurs, depending on…

Analysis of PDEs · Mathematics 2025-01-22 Jean-Baptiste Casteras , Leonard Monsaingeon , Luca Nenna

We consider the motion of a particle in a force field subjected to adiabatic, fluctuations of external origin. We do not put the restriction on the type of stochastic process that the noise is Gaussian. Based on a method developed earlier…

Statistical Mechanics · Physics 2007-05-23 Suman Kumar Banik , Jyotipratim Ray Chaudhuri , Deb Shankar Ray

We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as in a finite interval. In the infinite…

We revisit the problem of diffusion in a driven system consisting of an inertial Brownian particle moving in a symmetric periodic potential and subjected to a symmetric time-periodic force. We reveal parameter domains in which diffusion is…

Statistical Mechanics · Physics 2022-11-23 I. G. Marchenko , A. Zhiglo , V. Aksenova , V. Tkachenko , I. I. Marchenko , J. Łuczka , J. Spiechowicz

The stochastic motion of a particle with long-range correlated increments (the moving phase) which is intermittently interrupted by immobilizations (the traping phase) in a disordered medium is considered in the presence of an external…

Statistical Mechanics · Physics 2023-08-31 Yingjie Liang , Wei Wang , Ralf Metzler

The exit problem for small perturbations of a dynamical system in a domain is considered. It is assumed that the unperturbed dynamical system and the domain satisfy the Levinson conditions. We assume that the random perturbation affects the…

Probability · Mathematics 2010-06-15 Sergio Angel Almada Monter , Yuri Bakhtin

The main result in this paper is a variational formula for the exit rate from a bounded domain for a diffusion process in terms of the stationary law of the diffusion constrained to remain in this domain forever. Related results on the…

Probability · Mathematics 2020-03-17 Ari Arapostathis , Vivek S. Borkar

We investigate the Kramers escape from a potential well of a test particle driven by fractional Gaussian noise with Hurst exponent 0<H<1. From a numerical analysis we demonstrate the exponential distribution of escape times from the well…

The Active Brownian Particle (ABP) model has become a prototype of self-propelled particles. ABPs move persistently at a constant speed $V$ along a direction that changes slowly by rotational diffusion, characterized by a coefficient $\Dr$.…

Soft Condensed Matter · Physics 2025-03-11 Rodrigo Soto

Overdamped Brownian motion of a self-propelled particle is studied by solving the Langevin equation analytically. On top of translational and rotational diffusion, in the context of the presented model, the "active" particle is driven along…

Soft Condensed Matter · Physics 2013-05-15 Borge ten Hagen , Sven van Teeffelen , Hartmut Löwen

A large deviation principle is established for a two-scale stochastic system in which the slow component is a continuous process given by a small noise finite dimensional It\^{o} stochastic differential equation, and the fast component is a…

Probability · Mathematics 2017-05-09 Amarjit Budhiraja , Paul Dupuis , Arnab Ganguly

Thermally activated escape of a Brownian particle over a potential barrier is well understood within Kramers theory. When subjected to an external magnetic field, the Lorentz force slows down the escape dynamics via a rescaling of the…

Statistical Mechanics · Physics 2022-08-10 Iman Abdoli , Jens-Uwe Sommer , Hartmut Löwen , Abhinav Sharma

Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle,…

Probability · Mathematics 2018-06-25 Pierre Mathieu , Andrey Piatnitski

This article concerns the large deviations regime and the consequent solution of the Kramers problem for a two-time scale stochastic system driven by a common jump noise signal perturbed in small intensity $\varepsilon>0$ and with…

Probability · Mathematics 2022-07-15 Pedro Catuogno , André de Oliveira Gomes

In this paper we consider a diffusion process obtained as a small random perturbation of a dynamical system attracted to a stable equilibrium point. The drift and the diffusive perturbation are assumed to evolve slowly in time. We describe…

Probability · Mathematics 2016-10-23 Mark Freidlin , Leonid Koralov

We discuss recent work on the static and dynamical properties of the asymmetric exclusion process, generalized to include the effect of disorder. We study in turn: random disorder in the properties of particles; disorder in the spatial…

Statistical Mechanics · Physics 2009-11-11 Mustansir Barma