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A discrete model of traffic on a multilane road is considered. The traffic is presented as particles movement with a deterministic component and a stochastic one. Formulas for the traffic characteristics have been found. The model can…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
A discrete-time totally asymmetric simple exclusion process on a lattice with open boundaries is considered. There are particles of different types. The type of a particle is characterized by the probability that a particle moves to a…
We present the idea of intertwining of two diffusions by Feynman-Kac operators. We present some variations and implications of the method and give examples of its applications. Among others, it turns out to be a very useful tool for finding…
We discuss variational formulas for the limits of certain models of motion in a random medium: namely, the limiting time constant for last-passage percolation and the limiting free energy for directed polymers. The results are valid for…
A granular gas composed of inelastic hard spheres or disks in the homogeneous cooling state is considered. Some of the particles are labeled and their number density exhibits a time-independent linear profile along a given direction. As a…
We develop a systematic method to obtain the solution of the collisionless Boltzmann equation which describes the growth of large-scale structures as a perturbative series over the initial density perturbations. We give an explicit…
We uncover a duality between relaxation and first passage processes in ergodic reversible Markovian dynamics in both discrete and continuous state-space. The duality exists in the form of a spectral interlacing -- the respective time scales…
We study a version of first passage percolation on $\mathbb{Z}^d$ where the random passage times on the edges are replaced by contact times represented by random closed sets on $\mathbb{R}$. Similarly to the contact process without…
We introduce driven exclusion processes with internal states that serve as generic transport models in various contexts, ranging from molecular or vehicular traffic on parallel lanes to spintronics. The ensuing non-equilibrium steady states…
Spatially distributed problems are often approximately modelled in terms of partial differential equations (PDEs) for appropriate coarse-grained quantities (e.g. concentrations). The derivation of accurate such PDEs starting from finer…
We model chaotic diffusion, in a symplectic 4D map by using the result of a theorem that was developed for stochastically perturbed integrable Hamiltonian systems. We explicitly consider a map defined by a free rotator (FR) coupled to a…
Auto encoding models have been extensively studied in recent years. They provide an efficient framework for sample generation, as well as for analysing feature learning. Furthermore, they are efficient in performing interpolations between…
Sampling viable 3D structures (e.g., molecules and point clouds) with SE(3)-invariance using diffusion-based models proved promising in a variety of real-world applications, wherein SE(3)-invariant properties can be naturally characterized…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
In this paper, we construct the Bessel line ensemble, a countable collection of continuous random curves. This line ensemble is stationary under horizontal shifts with the Bessel point process as its one-time marginal. Its finite…
One-dimensional asymmetric simple exclusion processes (ASEPs) which are coupled to external reservoirs via diffusive transport are studied. These ASEPs consist of active compartments characterized by directed movements of the particles and…
This is the second, and last paper in which we address the behavior of oriented first passage percolation on the hypercube in the limit of large dimensions. We prove here that the extremal process converges to a Cox process with exponential…
The paper identifies families of quasi-stationary initial conditions for infinite Brownian particle systems within a large class and provides a construction of the particle systems themselves started from such initial conditions. Examples…
The Inverse First Passage time problem seeks to determine the boundary corresponding to a given stochastic process and a fixed first passage time distribution. Here, we determine the numerical solution of this problem in the case of a two…