Related papers: Area Distribution of Elastic Brownian Motion
Statistical properties of Brownian motion that arise by analyzing, separately, trajectories over which the system energy increases (upside) or decreases (downside) with respect to a threshold energy level, are derived. This selective…
A Brownian motion model is proposed to study parametric correlations in the transmission eigenvalues of open ballistic cavities. We find interesting universal properties when the eigenvalues are rescaled at the hard edge of the spectrum. We…
When random walks on a square lattice are biased horizontally to move solely to the right, the probability distribution of their algebraic area can be exactly obtained. We explicitly map this biased classical random system on a non…
Consider a generic triangle in the upper half of the complex plane with one side on the real line. This paper presents a tailored construction of a discrete random walk whose continuum limit is a Brownian motion in the triangle, reflected…
We focus on the dynamics of a Brownian particle whose mass fluctuates. First we show that the behaviour is similar to that of a Brownian particle moving in a fluctuating medium, as studied by Beck [Phys. Rev. Lett. 87 (2001) 180601]. By…
Activity significantly enhances the escape rate of a Brownian particle over a potential barrier. Whereas constant activity has been extensively studied in the past, little is known about the effect of time-dependent activity on the escape…
We study the position distribution of a single active Brownian particle (ABP) on the plane. We show that this distribution has a compact support, the boundary of which is an expanding circle. We focus on a short-time regime and employ the…
We consider a model of Branching Brownian Motion in which the usual spatially-homogeneous and catalytic branching at a single point are simultaneously present. We establish the almost sure growth rates of population in certain…
We find the exponential growth rate of the population outside a ball with time dependent radius for a branching Brownian motion in Euclidean space. We then see that the upper bound of the particle range is determined by the principal…
The Brownian force model (BFM) is a mean-field model for the local velocities during avalanches in elastic interfaces of internal space dimension $d$, driven in a random medium. It is exactly solvable via a non-linear differential equation.…
Several Brownian areas are considered in this paper: the Brownian excursion area, the Brownian bridge area, the Brownian motion area, the Brownian meander area, the Brownian double meander area, the positive part of Brownian bridge area,…
Sticky Brownian motion on the real line can be obtained as a weak solution of a system of stochastic differential equations. We find the conditional distribution of the process given the driving Brownian motion, both at an independent…
The area swept out under a one-dimensional Brownian motion till its first-passage time is analysed using a backward Fokker-Planck technique. We obtain an exact expression of the area distribution for the zero drift case, and provide various…
We consider an active Brownian particle moving in a disordered two-dimensional energy or motility landscape. The averaged mean-square-displacement (MSD) of the particle is calculated analytically within a systematic short-time expansion. As…
Fractional Brownian motion, a Gaussian non-Markovian self-similar process with stationary long-correlated increments, has been identified to give rise to the anomalous diffusion behavior in a great variety of physical systems. The…
We consider the occupation area of spherical (fractional) Brownian motion, i.e. the area where the process is positive, and show that it is uniformly distributed. For the proof, we introduce a new simple combinatorial view on occupation…
We study the position distribution of an active Brownian particle (ABP) in the presence of stochastic resetting in two spatial dimensions. We consider three different resetting protocols : (I) where both position and orientation of the…
We consider a one-dimensional Brownian motion of fixed duration $T$. Using a path-integral technique, we compute exactly the probability distribution of the difference $\tau=t_{\min}-t_{\max}$ between the time $t_{\min}$ of the global…
The exact analytical expressions for the time-dependent cross-correlations of the translational and rotational Brownian displacements of a particle with arbitrary shape were derived by us in [J. Chem. Phys. 142, 214902 (2015) and 144,…
We construct a two-dimensional diffusion process with rank-dependent local drift and dispersion coefficients, and with a full range of patterns of behavior upon collision that range from totally frictionless interaction, to elastic…