Related papers: Linear and superlinear spread for continuous-time …
Random walks find applications in many areas of science and are the heart of essential network analytic tools. When defined on temporal networks, even basic random walk models may exhibit a rich spectrum of behaviours, due to the…
We consider the problem of leakage or effusion of an ensemble of independent stochastic processes from a region where they are initially randomly distributed. The case of Brownian motion, initially confined to the left half line with…
The propagation of an initially localized excitation in one dimensional incommensurate, quasiperiodic and random systems is investigated numerically. It is discovered that the time evolution of variances $\sigma^2(t)$ of atom displacements…
We investigate the dynamics of tracer particles in the random average process (RAP), a single-file system in one dimension. In addition to the position, every particle possesses an internal spin variable $\sigma (t)$ that can alternate…
We study the stochastic dynamics of a particle with two distinct motility states. Each one is characterized by two parameters: one represents the average speed and the other represents the persistence quantifying the tendency to maintain…
Contacts between individuals serve as pathways where infections may propagate. These contact patterns can be represented by network structures. Static structures have been the common modeling paradigm but recent results suggest that…
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…
The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…
There are various cases of animal movement where behaviour broadly switches between two modes of operation, corresponding to a long distance movement state and a resting or local movement state. Here a mathematical description of this…
We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. This model is known to exhibit a phase transition: If $d \ge 3$ and the environment is "not too random", then, the total…
The quantum walk is a quantum counterpart of the classical random walk that exhibits nonclassical behaviors and outperforms the classical random walk in various aspects. It has been known that a single particle can be propagated by a…
Experiments on particles' motion in living cells show that it is often subdiffusive. This subdiffusion may be due to trapping, percolation-like structures, or viscoelatic behavior of the medium. While the models based on trapping (leading…
We consider a random walk on the support of a stationary simple point process on $R^d$, $d\geq 2$ which satisfies a mixing condition w.r.t.the translations or has a strictly positive density uniformly on large enough cubes. Furthermore the…
We consider a two-type reducible branching Brownian motion, defined as a particle system on the real line in which particles of two types move according to independent Brownian motion and create offspring at constant rate. Particles of type…
Spider walks are systems of interacting particles. The particles move independently as long as their movement do not violate some given rules describing the relative position of the particles; moves that violate the rules are not realized.…
Monte Carlo (MC) simulations of transport in random porous networks indicate that for high variances of the log-normal permeability distribution, the transport of a passive tracer is non-Fickian. Here we model this non-Fickian dispersion in…
For n + 1 particles moving independently on a straight line, we study the question of how long the leading position of one of them can last. Our focus is the asymptotics of the probability p(T,n) that the leader time will exceed T when n…
We consider the TASEP on Z with two blocks of particles having different jump rates. We study the large time behavior of particles' positions. It depends both on the jump rates and the region we focus on, and we determine the complete…
What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals $\tau$ distributed as a power-law $\sim \tau^{-(1+\alpha)};\alpha>0$? Modeling the stochastic process by diffusion and the…
We study the frog model on Cayley graphs of groups with polynomial growth rate $D \geq 3$. The frog model is an interacting particle system in discrete time. We consider that the process begins with a particle at each vertex of the graph…