相关论文: The shape theorem for the frog model

Understanding how biological and synthetic systems achieve robust function in noisy environments remains a fundamental challenge across the physical and life sciences. To connect robust behavior with non-trivial topological features present…

We investigate the dynamics of a particle executing a general Continuous Time Random Walk (CTRW) in three dimensions under the influence of arbitrary time-varying external fields. Contrary to the general approach in recent works, our method…

Run-and-tumble particles (RTPs) have emerged as a paradigmatic example for studying nonequilibrium phenomena in statistical mechanics. The invariant measure of a wide class of RTPs subjected to a potential possesses a density that is…

In the present paper, we introduce and analyze elephant random walks (ERWs) on bipartite periodic lattices arising as coverings of dipole graphs. We focus on lattices whose admissible step directions in the two parts of the bipartition are…

A simple object (one point in $m$-dimensional space) is the resultant of the evolving matrix polynomial of walks in the irreducible aperiodic network structure of the first order DeGroot (weighted averaging) state-space process. This paper…

We consider random walks in which the walk originates in one set of nodes and then continues until it reaches one or more nodes in a target set. The time required for the walk to reach the target set is of interest in understanding the…

This article introduces a model for interacting vertex-reinforced random walks, each taking values on a complete sub-graph of a locally finite undirected graph. The transition probability for a walk to a given vertex depends on the…

We consider the long-time behaviour of binary branching Brownian motion (BBM) where the branching rate depends on a periodic spatial heterogeneity. We prove that almost surely as $t\to\infty$, the heterogeneous BBM at time $t$, normalized…

We consider random walkers that deform the medium as they move, enabling a faster motion in regions which have been recently visited. This induces an effective attraction between walkers mediated by the medium, which can be regarded as a…

Emergence is a concept that is easy to exhibit, but very hard to formally handle. This paper is about cubic sand grains moving around on nicely packed columns in one dimension (the physical sandpile is two dimensional, but the support of…

We present a general approach to study a class of random growth models in $n$-dimensional Euclidean space. These models are designed to capture basic growth features which are expected to manifest at the mesoscopic level for several…

In this paper we study the behavior of a continuous time random walk (CTRW) on a stationary and ergodic time varying dynamic graph. We establish conditions under which the CTRW is a stationary and ergodic process. In general, the stationary…

We illustrate shape mode analysis as a simple, yet powerful technique to concisely describe complex biological shapes and their dynamics. We characterize undulatory bending waves of beating flagella and reconstruct a limit cycle of…

The combined Continuous Time Random Walk (CTRW) in position and momentum space is introduced, in the form of two coupled integral equations that describe the evolution of the probability distribution for finding a particle at a certain…

We consider a nearest neighbor random walk on the one-dimensional integer lattice with drift towards the origin determined by an asymptotically vanishing function of the number of visits to zero. We show the existence of distinct regimes…

Diagonal or chevron patterns are known to spontaneously emerge at the intersection of two perpendicular flows of self-propelled particles, e.g. pedestrians. The instability responsible for this pattern formation has been studied in previous…

The rotor walk is a derandomized version of the random walk on a graph. On successive visits to any given vertex, the walker is routed to each of the neighboring vertices in some fixed cyclic order, rather than to a random sequence of…

Random walks on five-dimensional potential-energy surfaces were recently found to yield fission-fragment mass distributions that are in remarkable agreement with experimental data. Within the framework of the Smoluchowski equation of…

This paper concerns the long term behaviour of a growth model describing a random sequential deposition of particles on a finite graph. The probability of allocating a particle at a vertex is proportional to a log-linear function of numbers…

This paper presents results from a flow visualization study of the wake structures behind solid spheres rising or falling freely in liquids under the action of gravity. These show remarkable differences to the wake structures observed…