Related papers: An aspect of particles' spatial competition
In this article, we study a type of a one dimensional percolation model whose basic features include a sequential dropping of particles on a substrate followed by their transport via a pushing mechanism (see [S. N. Majumdar and D. S. Dean,…
The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…
We consider transport of passive particles in steady laminar plane flows of incompressible viscous fluids. While drifting along the streamlines, the particles experience alternating accelerations and slowdowns. For an ensemble of particles,…
Based on experimental observations it is known that various biological cells exhibit a persistent random walk during migration on flat substrates. The persistent random walk is characterized by `stop-and-go' movements : unidirectional…
We consider a discrete-time branching random walk defined on the real line, which is assumed to be supercritical and in the boundary case. It is known that its leftmost position of the $n$-th generation behaves asymptotically like…
The fourfold research proposal regards in particular: critical oriented percolation; random walk limit laws; neural networks with long-range connections; the ant in a labyrinth.
We discovered that when a pair of small particles is optically levitated, the particles execute a dance whose motion resembles the orbits of balls being juggled. This motion lies in a plane perpendicular to the polarization of the incident…
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…
We consider the following interacting particle system: There is a ``gas'' of particles, each of which performs a continuous time simple random walk on the d-dimensional lattice. These particles are called A-particles and move independently…
We show that the transience or recurrence of a random walk in certain random environments on an arbitrary infinite locally finite tree is determined by the branching number of the tree, which is a measure of the average number of branches…
Movements of molecular motors on cytoskeletal filaments are described by directed walks on a line. Detachment from this line is allowed to occur with a small probability. Motion in the surrounding fluid is described by symmetric random…
Discrete-time quantum walks, quantum generalizations of classical random walks, provide a framework for quantum information processing, quantum algorithms and quantum simulation of condensed matter systems. The key property of quantum…
The transport of high-energy particles in the presence of small-scale, turbulent magnetic fields is a long-standing issue in astrophysics. Analytical theories on transport perpendicular to the large-scale magnetic field disagree with…
For a set $A\subset C[0,\infty)$, we give new results on the growth of the number of particles in a dyadic branching Brownian motion whose paths fall within A. We show that it is possible to work without rescaling the paths. We give large…
When confined to a topological environment consisting of a cycle coupled with a half-line, quantum walks exhibit long-term statistical tendencies which differ dramatically from the tendencies of classical random walks in the same…
The symmetric birth and death process in the integers $\{1, \ldots, N \}$ with linear rates is studied. The process moves slowly and spends more time in the neighborhood of the state 1. It represents our attempt at explaining the asymmetry…
Simple random walks on a partially directed version of $\mathbb{Z}^2$ are considered. More precisely, vertical edges between neighbouring vertices of $\mathbb{Z}^2$ can be traversed in both directions (they are undirected) while horizontal…
We consider the model of branching Brownian motion with a single catalytic point at the origin and binary branching. We establish some fine results for the asymptotic behaviour of the numbers of particles travelling at different speeds and…
We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition…
We study several fundamental properties of a class of stochastic processes called spatial Lambda-coalescents. In these models, a number of particles perform independent random walks on some underlying graph G. In addition, particles on the…