Related papers: Probability Law For the Euclidean Distance Between…
In this paper, we consider a subclass of piecewise deterministic Markov processes with a Polish state space that involve a deterministic motion punctuated by random jumps, occurring in a Poisson-like fashion with some state-dependent rate,…
Consider a one-dimensional branching Brownian motion, and rescale the coordinate and time so that the rates of branching and diffusion are both equal to $1$. If $X_1(t)$ is the position of the rightmost particle of the branching Brownian…
Original paper: We revisit the probability that any two consecutive events in a Poisson process N on [0,t] are separated by a time interval which is greater than s(<t) (a particular scan statistic probability), and the closely related…
We study the distributions of traveling length l and minimal traveling time t through two-dimensional percolation porous media characterized by long-range spatial correlations. We model the dynamics of fluid displacement by the convective…
We consider the general branching random walk under minimal assumptions, which in particular guarantee that the empirical particle distribution admits an almost sure central limit theorem. For such a process, we study the large time decay…
The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…
For one-dimensional Jump-Drift and Jump-Diffusion processes converging towards some steady state, the large deviations of a long dynamical trajectory are described from two perspectives. Firstly, the joint probability of the empirical…
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schr\"{o}dinger equation or wavefunctions. Unlike the standard QM…
Given a symmetric random walk in $Z^2$ with finite second moments, let $R_n$ be the range of the random walk up to time $n$. We study moderate deviations for $R_n -E R_n$ and $E R_n -R_n$. We also derive the corresponding laws of the…
In this paper we create a model of particle motion on a three-dimensional lattice using discrete random walk with small steps. We rigorously construct a probability space of the particle trajectories. Unlike deterministic approach in…
We use a Bayesian approach to derive the distance probability distribution for one object from its parallax with measurement uncertainty for two spatial distribution priors, viz. a homogeneous spherical distribution and a galactocentric…
Dynamics of a classical particle in a one-dimensional, randomly driven potential is analysed both analytically and numerically. The potential considered here is composed of two identical spatially-periodic saw-tooth-like components, one of…
Consider a branching Brownian motion (BBM). It is well known \cite{Bramson1983ConvergenceOS, Lalley1987ACL} that the rightmost particle is located near \( m_t = \sqrt{2} t - \frac{3}{2\sqrt{2}} \log t \). Let $\mathcal{N}(t,x)$ be the set…
We define the probability structure of a continuous-time time-homogeneous Markov jump process, on a finite graph, that represents the continuous-time counterpart of the so-called Ruelle-Bowen discrete-time random walk. It constitutes the…
A flowing pair of particles in inertial microfluidics gives important insights into understanding and controlling the collective dynamics of particles like cells or droplets in microfluidic devices. They are applied in medical cell analysis…
We consider an analogue of the Kac random walk on the special orthogonal group $SO(N)$, in which at each step a random rotation is performed in a randomly chosen 2-plane of $\bR^N$. We obtain sharp asymptotics for the rate of convergence in…
This contribution presents a derivation of the steady-state distribution of velocities and distances of driven particles on a onedimensional periodic ring. We will compare two different situations: (i) symmetrical interaction forces…
Quantum walks and random walks bear similarities and divergences. One of the most remarkable disparities affects the probability of finding the particle at a given location: typically, almost a flat function in the first case and a…
In a system made up of independent random walks, fluctuations of order $n^{1/4}$ from the hydrodynamic limit come from particle current across characteristics. We show that a two-parameter space-time particle current process converges to a…
The paper is devoted to the relationship between the continuous Markovian description of Levy flights developed previously and their equivalent representation in terms of discrete steps of a wandering particle, a certain generalization of…