Related papers: Large Deviation Function for a Driven Underdamped …
Exact and asymptotic formulas relating to dynamical correlations for overdamped Brownian motion are obtained. These formulas include a generalization of the $f$-sum rule from the theory of quantum fluids, a formula relating the static…
Trajectories of an overdamped particle in a highly unstable potential diverge so rapidly, that the variance of position grows much faster than its mean. Description of the dynamics by moments is therefore not informative. Instead, we…
A Brownian particle moving in a staircase-like potential with feedback control offers a way to implement Maxwell's demon. An experimental demonstration of such a system using sinusoidal periodic potential carried out by Toyabe et al. has…
We consider the two dimensional motion of a particle into a confining potential, subjected to Brownian forces, associated with two different temperatures on the orthogonal directions. Exact solutions are obtained for an asymmetric harmonic…
The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic…
In active Brownian motion, an internal propulsion mechanism interacts with translational and rotational thermal noise and other internal fluctuations to produce directed motion. We derive the distribution of its extreme fluctuations and…
This work is concerned with the large deviation principle for a family of slow-fast systems perturbed by infinite-dimensional mixed fractional Brownian motion with Hurst parameter $H\in(\frac12,1)$. We adopt the weak convergence method…
We study the fluctuation properties of the local time density, ${\rho _T} = \frac{1}{T}\int_0^T {\delta ( {r(t) - 1} )} dt$, spent by a $d$-dimensional Brownian particle at a spherical shell of unit radius, where $r(t)$ denotes the radial…
The large deviation function has been known for a long time in the literature for the displacement of the rightmost particle in a branching random walk (BRW), or in a branching Brownian motion (BBM). More recently a number of…
We investigate the stochastic motion of a Brownian particle in the harmonic potential with a time-dependent force constant. It may describe the motion of a colloidal particle in an optical trap where the potential well is formed by a…
We study the large deviation function for the entropy production rate in two driven one-dimensional systems: the asymmetric random walk on a discrete lattice and Brownian motion in a continuous periodic potential. We compare two approaches:…
We study the long-time behavior of underdamped Brownian particle moving through a viscous medium and in a systematic potential, when it is subjected to a space-dependent high-frequency periodic force. When the frequency is very large, much…
We prove a Large Deviations Principle (LDP) for systems of diffusions (particles) interacting through their ranks, when the number of particles tends to infinity. We show that the limiting particle density is given by the unique solution of…
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…
We analyse large deviations of the dynamical activity in one-dimensional systems of diffusing hard particles. Using an optimal-control representation of the large-deviation problem, we analyse effective interaction forces which can be added…
Large deviation functions are an essential tool in the statistics of rare events. Often they can be obtained by contraction from a so-called level 2 large deviation {\em functional} characterizing the empirical density of the underlying…
We establish large deviation principles (LDPs) for empirical measures associated with a sequence of Gibbs distributions on $n$-particle configurations, each of which is defined in terms of an inverse temperature $% \beta_n$ and an energy…
We present an efficient method to perform overdamped Brownian dynamics simulations in external force fields and for particle interactions that include a hardcore part. The method applies to particle motion in one dimension, where it is…
Extensive time-series encoding the position of particles such as viruses, vesicles, or individual proteins are routinely garnered in single-particle tracking experiments or supercomputing studies. They contain vital clues on how viruses…
We discuss physical and mathematical aspects of the over-damped motion of a Brownian particle in fluctuating potentials. It is shown that such a system can be described quantitatively by fluctuating rates if the potential fluctuations are…