Related papers: Dyson Brownian motion on a Jordan curve
The interplay between Coulomb friction and random excitations is studied experimentally by means of a rotating probe in contact with a stationary granular gas. The granular material is independently fluidized by a vertical shaker, acting as…
Quantum Brownian motion in the strong friction limit is studied based on the exact path integral formulation of dissipative systems. In this limit the time-nonlocal reduced dynamics can be cast into an effective equation of motion, the…
A covariant Fokker-Planck type equation for a simple gas and an equation for the Brownian motion are derived from a relativistic kinetic theory based on the Boltzmann equation. For the simple gas the dynamic friction four-vector and the…
We consider the hydrodynamic limit in the macroscopic regime of the coupled system of stochastic differential equations, $ d\lambda_t^i=\frac{1}{\sqrt{N}} dW_t^i - V'(\lambda_t^i) dt+ \frac{\beta}{2N} \sum_{j\not=i}…
We extend the Poincar\'{e}--Borel lemma to a weak approximation of a Brownian motion via simple functionals of uniform distributions on n-spheres in the Skorokhod space $D([0,1])$. This approach is used to simplify the proof of the…
We derive a quantum master equation from first principles to describe friction in one dimensional, collisional Brownian motion. We are the first to avoid an ill-defined square of the Dirac delta function by using localized wave packets…
We investigate stochastic processes that generalize geometric Brownian motion, focusing on cases where the standard invariant measure, i.e. the solution of the stationary Fokker-Planck equation does not necessarily exist. We demonstrate…
This paper investigates the probability distribution of solutions to McKean--Vlasov stochastic differential equations driven by fractional Brownian motion with Hurst parameter H>1/2. Our main contribution is the derivation of the associated…
The classical Jordan curve theorem for digital curves asserts that the Jordan curve theorem remains valid in the Khalimsky plane. Since the Khalimsky plane is a quotient space of $\mathbb R^2$ induced by a tiling of squares, it is natural…
We investigate the stochastic dynamics of one sedimenting active Brownian particle in three dimensions under the influence of gravity and passive fluctuations in the translational and rotational motion. We present an analytical solution of…
This case study proposes robustness quantifications of many classical sample path properties of Brownian motion in terms of the (mean) deviation frequencies along typical a.s.~approximations. This includes L\'evy's construction of Brownian…
The covariant form of the multivariable diffusion-drift process is described by the covariant Fokker--Planck equation using the standard toolbox of Riemann geometry. The covariant form of the equivalent Langevin stochastic differential…
We propose a Langevin equation for systems in an environment with nonuniform temperature. At odds with an older proposal, ours admits a locally Maxwellian steady state, local equipartition holds and for detailed-balanced (reversible)…
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…
In this paper, the first microscopic approach to the Brownian motion is developed in the case where the mass density of the suspending bath is of the same order of magnitude as that of the Brownian (B) particle. Starting from an extended…
Motivated by subdiffusive motion of bio-molecules observed in living cells we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and…
Based upon the Smoluchowski equation on curved manifolds three physical observables are considered for the Brownian displacement, namely, geodesic displacement, $s$, Euclidean displacement, $\delta{\bf R}$, and projected displacement…
Dynamics simulations of constrained particles can greatly aid in understanding the temporal and spatial evolution of biological processes such as lateral transport along membranes and self-assembly of viruses. Most theoretical efforts in…
The Brownian motion of a test particle interacting with a quantum scalar field in the presence of a perfectly reflecting boundary is studied in (1 + 1)-dimensional flat spacetime. Particularly, the expressions for dispersions in velocity…
The random motion of a Brownian particle confined in some finite domain is considered. Quite generally, the relevant statistical properties involve infinite series, whose coefficients are related to the eigenvalues of the diffusion…