Related papers: Trapping planar Brownian motion in a non circular …
Consider a large system of $N$ Brownian motions in $\R ^d$ fixed on a time interval $[0,\beta]$ with symmetrized initial and terminal conditions, under the influence of a trap potential. Such systems describe systems of bosons at positive…
Given a Brownian path $\beta(t)$ on $\mathbb{R}$, starting at $1$, a.s. there is a singular time set $T_{\beta}$, such that the first hitting time of $\beta$ by an independent Brownian motion, starting at $0$, is in $T_{\beta}$ with…
We study a space-time Brownian motion with drift B(t)=(t_0+t,y_0+W(t)+t) killed at the moving boundary of the cone {(t,x):0<x<t}. This article determines the parabolic Martin boundary and all harmonic functions associated with this process.…
Consider a negatively drifted one dimensional Brownian motion starting at positive initial position, its first hitting time to 0 has the inverse Gaussian law. Moreover, conditionally on this hitting time, the Brownian motion up to that time…
We study a one-dimensional Brownian motion conditioned on a self-repelling behaviour. Given a nondecreasing positive function f(t), consider the measures mu_t obtained by conditioning a Brownian path so that L_s< f(s), for all s<t, where…
We propose a macroscopic realization of planar Brownian motion by vertically vibrated disks. We perform a systematic statistical analysis of many random trajectories of individual disks. The distribution of increments is shown to be almost…
By using the law of the excursions of Brownian motion with drift, we find the distribution of the $n-$th passage time of Brownian motion through a straight line $S(t)= a + bt.$ In the special case when $b = 0,$ we extend the result to a…
A Brownian loop is a random walk circuit of infinitely many, suitably infinitesimal, steps. In a plane such a loop may or may not enclose a marked point, the origin, say. If it does so it may wind arbitrarily many times, positive or…
Non-adiabatic motion of Bose-Einstein condensates of rubidium atoms arising from the dynamical nature of a time-orbiting-potential (TOP) trap was observed experimentally. The orbital micromotion of the condensate in velocity space at the…
A result of R. Durrett, D. Iglehart and D. Miller states that Brownian meander is Brownian motion conditioned to stay positive for a unit of time, in the sense that it is the weak limit, as $x$ goes to 0, of Brownian motion started at $x>0$…
We present an interesting connection between Brownian motion and magnetism. We use this to determine the distribution of areas enclosed by the path of a particle diffusing on a sphere. In addition, we find a bound on the free energy of an…
We describe a simple numerical simulation, suitable for an undergraduate project (or graduate problem set), of the Brownian motion of a particle in a Hooke-law potential well. Understanding this physical situation is a practical necessity…
Experimental and theoretical studies are made of Brownian particles trapped in a periodic potential, which is very slightly tilted due to gravity. In the presence of fluctuations, these will trigger a measurable average drift along the…
In the past few years, stochastic resetting has become a subject of immense interest. Most of the theoretical studies so far focused on instantaneous resetting which is, however, a major impediment to practical realization or experimental…
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…
The classical model that describes the motion of an atom in a magnetic trap is solved in order to investigate the relationship between the failure of the usual adiabatic approximation assumption and the physical parameters of the trap. This…
We consider the model of the Brownian plane, which is a pointed non-compact random metric space with the topology of the complex plane. The Brownian plane can be obtained as the scaling limit in distribution of the uniform infinite planar…
We derive explicit formulas for probabilities of Brownian motion with jumps crossing linear or piecewise linear boundaries in any finite interval. We then use these formulas to approximate the boundary crossing probabilities for general…
It is known that obstacles can hydrodynamically trap bacteria and synthetic microswimmers in orbits, where the trapping time heavily depends on the swimmer flow field and noise is needed to escape the trap. Here, we use experiments and…
Brownian systems are characterized by spatiotemporal disorder, which arises from the erratic motion of particles driven by thermal fluctuations. When light interacts with such systems, it typically produces unpolarized and uncorrelated…