Related papers: Meteor process on ${\mathbb Z}^d$
Many real transportation and mobility networks have their vertices placed on the surface of the Earth. In such embeddings, the edges laid on that surface may cross. In his pioneering research, Moon analyzed the distribution of the number of…
We consider the time evolution of the supercritical Galton-Watson model of branching particles with extra parameter (mass). In the moment of the division the mass of the particle (which is growing linearly after the birth) is divided in…
In first-passage percolation, one places nonnegative i.i.d. random variables (T(e)) on the edges of Z^d. A geodesic is an optimal path for the passage times T(e). Consider a local property of the time environment. We call it a pattern. We…
Scattering transforms are a new type of summary statistics recently developed for the study of highly non-Gaussian processes, which have been shown to be very promising for astrophysical studies. In particular, they allow one to build…
We consider the averaging process on a graph, that is the evolution of a mass distribution undergoing repeated averages along the edges of the graph at the arrival times of independent Poisson processes. We establish cutoff phenomena for…
The voter model on $\mathbb{Z}^d$ is a particle system that serves as a rough model for changes of opinions among social agents or, alternatively, competition between biological species occupying space. When $d \geq 3$, the set of…
Context. Several authors predicted an outburst of the Draconid meteor shower in 2018, but with an uncertain level of activity. Aims. Optical meteor observations were used to derive the population and mass indices, flux, and radiant…
We develop a Markov process viewpoint for discrete circular distributions motivated by directional-statistics settings where angles are observed on a finite grid and evolve over time. On the $m$-point discrete circle, the cycle graph, we…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
A nonuniform system is considered consisting of two phases with different densities of particles. At each given time the distribution of the phases in space is chaotic: each phase filling a set of regions with random shapes and locations. A…
We analyze an idealized model for the transmission or flow of particles, or discrete packets of information, in a weight bearing branching hierarchical 2-D networks, and its variants. The capacities add hierarchically down the clusters.…
A diffusion process for charge distributions in a phase space is examined. The corresponding charge moves in a force field and under an action of a random field. There are the diffusion motions for coordinates and for momenta. In our model,…
This is an overview of recent research on meteors and the parent bodies from which they are produced. While many meteor showers result from material ejected by comets, two out of the three strongest annual showers (the Geminids and the…
Given a Poisson process on a bounded interval, its random geometric graph is the graph whose vertices are the points of the Poisson process and edges exist between two points if and only if their distance is less than a fixed given…
Scattering is a ubiquitous phenomenon which is observed in a variety of physical systems which span a wide range of length scales. The scattering matrix is the key quantity which provides a complete description of the scattering process.…
Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and…
Meteor showers and their outbursts are the dominant source of meteoroid impact risk to spacecraft on short time scales. Meteor shower prediction models depend on historical observations to produce accurate forecasts. However, the current…
Let $F$ be a probability distribution with support on the non-negative integers. A model is proposed for generating stationary simple graphs on $\mathbb{Z}$ with degree distribution $F$ and it is shown for this model that the expected total…
We introduce the concept of a Markov influence system (MIS) and analyze its dynamics. An MIS models a random walk in a graph whose edges and transition probabilities change endogenously as a function of the current distribution. This…
We discuss how spreading processes on temporal networks are impacted by the shape of their inter-event time distributions. Through simple mathematical arguments and toy examples, we find that the key factor is the ordering in which events…