相关论文: Distribution of the area enclosed by a 2D random w…

We study analytically the asymptotic behaviour of the average probability P(n,t) for the trajectory of a 2D Brownian particle wandering in the presence of randomly distributed traps to wind n times around a given point after a time t. It is…

In this paper, following earlier results in [2] we derive the asymptotic distribution as $t \to \infty$, of the excursion of Brownian motion straddling $t$, into an interval $(a,b)$, conditional on the event that there is such an excursion.

Asymptotic estimates of the hitting distribution of a long segment on the real axis for two dimensional random walks on ${\bf Z}^2$ of zero mean and finite variances are obtained: some are general and exhibit its apparent similarity to the…

In this paper, we derive the distribution of a two-dimensional (complex) random walk in which the angle of each step is restricted to a subset of the circle. This setting appears in various domains, such as in over-the-air computation in…

We consider a Brownian particle moving on a ring. We study the probability distributions of the total number of turns and the net number of counter-clockwise turns the particle makes till time t. Using a method based on the renewal…

Nearest neighbor random walks in the quarter plane that are absorbed when reaching the boundary are studied. The cases of positive and zero drift are considered. Absorption probabilities at a given time and at a given site are made…

The algebraic area probability distribution of closed planar random walks of length N on a square lattice is considered. The generating function for the distribution satisfies a recurrence relation in which the combinatorics is encoded. A…

An exact expression for the distribution of the area swept out by a drifted Brownian motion till its first-passage time is derived. A study of the asymptotic behaviour confirms earlier conjectures and clarifies their range of validity. The…

We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a…

Suppose a solid has a crack filled with a gas. If the crack reaches the surrounding medium, how long does it take the gas to diffuse out of the crack? Iterated Brownian motion serves as a model for diffusion in a crack. If \tau is the first…

We present a model of anomalous diffusion consisting of an ensemble of particles undergoing homogeneous Brownian motion except for confinement by randomly placed reflecting boundaries. For power-law distributed compartment sizes, we…

We study the probability distribution of the value of geometric Brownian motion at the stochastic observation time. It is known that the exponentially distributed observation time yields the distribution called the double Pareto…

The first of $N$ identical independently distributed (i.i.d.) Brownian trajectories that arrives to a small target, sets the time scale of activation, which in general is much faster than the arrival to the target of only a single…

Nonergodicity observed in single-particle tracking experiments is usually modeled by transient trapping rather than spatial disorder. We introduce models of a particle diffusing in a medium consisting of regions with random sizes and random…

In this paper we present a computation of the mean first-passage times both for a random walk in a discrete bounded lattice, between a starting site and a target site, and for a Brownian motion in a bounded domain, where the target is a…

Euclidean random matrices appear in a broad class of physical problems involving disorder. The problem of determining their spectra can be mapped, using the replica method, into the study of a scalar field theory with an interaction of the…

We derive asymptotics for the probability of the origin to be an extremal point of a random walk in R^n. We show that in order for the probability to be roughly 1/2, the number of steps of the random walk should be between e^{c n / log n}$…

The distribution of the first hitting time of a disc for the standard two dimensional Brownian motion is computed. By investigating the inversion integral of its Laplace transform we give fairy detailed asymptotic estimates of its density…

We consider a one dimensional random walk in random environment that is uniformly biased to one direction. In addition to the transition probability, the jump rate of the random walk is assumed to be spatially inhomogeneous and random. We…

We find an exact series solution for the steady-state probability distribution of a harmonically trapped active Brownian particle in two dimensions, in the presence of translational diffusion. This series solution allows us to efficiently…