Related papers: Probability Law For the Euclidean Distance Between…

A cyclic random motion at finite velocity with orthogonal directions is considered in the plane and in $\mathbb{R}^3$. We obtain in both cases the explicit conditional distributions of the position of the moving particle when the number of…

Consider the random set composed of particles initially distributed on Zd, d >= 2, according to a Poisson point process of intensity u > 0 and moving as independent simple symmetric random walks, the trap particles. We are interested in the…

We consider the symmetric simple exclusion system on $\mathbb{Z}^d$, $d \ge 2$, starting from a class of ``step'' initial conditions in which particles are constrained within a half-space. One may count the number $N_t$ of particles that…

We derive exact expressions for the probabilities that partly random hyperplanes separate two Euclidean balls. The probability that a fully random hyperplane separates two balls turns out to be significantly smaller than the corresponding…

In this paper we consider the Porous Medium Equation and establish a relationship between its Kompanets-Zel'dovich-Barenblatt solution $u(\xd,t), \xd\in \mathbb R^d,t>0$ and random flights. The time-rescaled version of $u(\xd,t)$ is the…

We study simple random walk on the uniform spanning tree on Z^2 . We obtain estimates for the transition probabilities of the random walk, the distance of the walk from its starting point after n steps, and exit times of both Euclidean…

It has been known that the distribution of the random distances between two uniformly distributed points within a convex polygon can be obtained based on its chord length distribution (CLD). In this report, we first verify the existing…

Suppose that $X$ is a simple random walk on $\Z_n^d$ for $d \geq 3$ and, for each $t$, we let $\U(t)$ consist of those $x \in \Z_n^d$ which have not been visited by $X$ by time $t$. Let $\tcov$ be the expected amount of time that it takes…

We study the persistent random walk of photons on a one-dimensional lattice of random asymmetric transmittances. Each site is characterized by its intensity transmittance t (t') for photons moving to the right (left) direction.…

We consider a system of independent one-dimensional random walks in a common random environment under the condition that the random walks are transient with positive speed $v_P$. We give upper bounds on the quenched probability that at…

We consider a discrete time simple symmetric random walk on Z^d, d>=1, where the path of the walk is perturbed by inserting deterministic jumps. We show that for any time n and any deterministic jumps that we insert, the expected number of…

In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density $\rho \in (0,\infty)$.…

In the framework of a stochastic picture for the one-dimensional branching Brownian motion, we compute the probability density of the number of particles near the rightmost one at a time $T$, that we take very large, when this extreme…

We consider the motion of a particle along the geodesic lines of the Poincar\`e half-plane. The particle is specularly reflected when it hits randomly-distributed obstacles that are assumed to be motionless. This is the hyperbolic version…

We study interacting particle systems on the real line which generalize the Hammersley process [D. Aldous and P. Diaconis, Prob. Theory Relat. Fields 103, 199-213 (1995)]. Particles jump to the right to a randomly chosen point between their…

We study the problem of generating a hyperplane tessellation of an arbitrary set $T$ in $\mathbb{R}^n$, ensuring that the Euclidean distance between any two points corresponds to the fraction of hyperplanes separating them up to a…

A particle entering a scattering and absorbing medium executes a random walk through a sequence of scattering events. The particle ultimately achieves first-passage, leaving the medium or it is absorbed. The Kubelka-Munk model describes a…

Focusing on a continuous-time quantum walk on $\mathbb{Z}=\left\{0,\pm 1,\pm 2,\ldots\right\}$, we analyze a probability distribution with which the quantum walker is observed at a position. The walker launches off at a localized state and…

Random walks of n steps taken into independent uniformly random directions in a d-dimensional Euclidean space (d larger than 1), are named Dirichlet when their step lengths are distributed according to a Dirichlet law. The latter continuous…

Let $(G,\mu)$ be a uniformly elliptic random conductance graph on $\mathbb{Z}^d$ with a Poisson point process of particles at time $t=0$ that perform independent simple random walks. We show that inside a cube $Q_K$ of side length $K$, if…