Related papers: The exit distribution for iterated Brownian motion…
The first part of this paper is devoted to the Brown measure of the product of the free unitary Brownian motion by an arbitrary free non negative operator. Our approach follows the one recently initiated by Driver-Hall-Kemp though there are…
Brownian motion is a central scientific paradigm. Recently, due to increasing efforts and interests towards miniaturization and small-scale physics or biology, the effects of confinement on such a motion have become a key topic of…
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…
Aiming to understand the distribution of fitness levels of individuals in a large population undergoing selection, we study the particle configurations of branching Brownian motion where each particle independently moves as Brownian motion…
Given a survival distribution on the positive half-axis and a Brownian motion, a solution of the inverse first-passage problem consists of a boundary so that the first passage time over the boundary has the given distribution. We show that…
The question how the extremal values of a stochastic process achieved on different time intervals are correlated to each other has been discussed within the last few years on examples of the running maximum of a Brownian motion, of a…
We investigate the dynamics of an inertial chiral active Brownian particle in the presence of a harmonic confinement. Through numerical simulation, we observe that when the harmonic frequency becomes comparable to the chiral frequency, the…
Let $\tau_{D}(Z) $ is the first exit time of iterated Brownian motion from a domain $D \subset \RR{R}^{n}$ started at $z\in D$ and let $P_{z}[\tau_{D}(Z) >t]$ be its distribution. In this paper we establish the exact asymptotics of…
Brownian motion of a particle with an arbitrary shape is investigated theoretically. Analytical expressions for the time-dependent cross-correlations of the Brownian translational and rotational displacements are derived from the…
We study the sharp order of integrability of the exit position of Brownian motion from the planar domains ${\cal P}_\alpha = \{(x,y)\in \bR\times \bR\colon x> 0, |y| < Ax^{\alpha}\}$, $0<\alpha<1$. Together with some simple good-$\lambda$…
The first-passage-time problem for a Brownian motion with alternating infinitesimal moments through a constant boundary is considered under the assumption that the time intervals between consecutive changes of these moments are described by…
This paper derives a complete analytical solution for the probability distribution of the configuration of a non-holonomic vehicle that moves in two spatial dimensions by satisfying the unicycle kinematic constraints and in presence of…
We investigate the behaviour of a finite chain of Brownian particles, interacting through a pairwise potential $U$, with one end of the chain fixed and the other end pulled away, in the limit of slow pulling speed and small Brownian noise.…
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 study the diffusion of Brownian particles on the surface of a sphere and compute the distribution of solid angles enclosed by the diffusing particles. This function describes the distribution of geometric phases in two state quantum…
We study the behaviour of a Brownian particle in the overdamped regime in the presence of a harmonic potential, assuming its diffusion coefficient to randomly jump between two distinct values. In particular, we characterize the probability…
We compute the Brown measure of $x_{0}+i\sigma_{t}$, where $\sigma_{t}$ is a free semicircular Brownian motion and $x_{0}$ is a freely independent self-adjoint element that is not a multiple of the identity. The Brown measure is supported…
We investigate the behaviour of a finite chain of Brownian particles, interacting through a pairwise quadratic potential, with one end of the chain fixed and the other end pulled away at slow speed, in the limit of slow speed and small…
In this short note we derive a closed form for the trivariate distribution (position, local time at the origin, and positive occupation time) of the one-dimensional sticky Brownian motion, thereby filling some gaps and fixing some mistakes…
We compute the joint distribution of the first times a linear diffusion makes an excursion longer than some given duration above (resp. below) some fixed level. In the literature, such stopping times have been introduced and studied in the…