Related papers: Comparison of two models of tethered motion
Nodes can be ranked according to their relative importance within the network. Ranking algorithms based on random walks are particularly useful because they connect topological and diffusive properties of the network. Previous methods based…
A new master equation to mimic the dynamics of a collection of interacting random walkers in an open system is proposed and solved numerically.In this model, the random walkers interact through excluded volume interaction (single-file…
A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…
We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. We prove an invariance principle (functional central limit theorem) under almost every fixed environment. The…
We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti-)persistence. We present an…
In this work we establish a link between two different phenomena that were studied in a large and growing number of biological, composite and soft media: the diffusion in compartmentalized environment and the Brownian yet non-Gaussian…
We consider two models of one-dimensional random walks among biased i.i.d. random conductances: the first is the classical exponential tilt of the conductances, while the second comes from the effect of adding an external field to a random…
We study a one-dimensional lattice random walk with an absorbing boundary at the origin and a movable partial reflector. On encountering the reflector, at site x, the walker is reflected (with probability r) to x-1 and the reflector is…
We study the statistical properties of trainable agents moving in discrete space. After introducing the mathematical framework, we first analyze the dynamics of two completely random walkers, mutually competing in a chaser-target…
We consider a one-dimensional simple random walk surviving among a field of static soft traps : each time it meets a trap the walk is killed with probability 1--e --$\beta$ , where $\beta$ is a positive and fixed parameter. The positions of…
We consider three kinds of discrete-time arrival processes: transient, intermediate and recurrent, characterized by a finite, possibly finite and infinite number of events, respectively. In this context, we study renewal processes which are…
A model of interacting random walkers is presented and shown to give rise to patterns consisting in periodic arrangements of fluctuating particle clusters. The model represents biological individuals that die or reproduce at rates depending…
The distribution of the first positive position reached by a random walker starting from the origin is fundamental for understanding the statistics of extremes and records in one-dimensional random walks. We present a comprehensive study of…
We use molecular dynamics simulations to investigate the tracer diffusion in a sea of polymers with specific binding zones for the tracer. These binding zones act as traps. Our simulations show that the tracer can undergo normal yet…
Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a…
We analyze a trapping reaction with a single penetrable trap, in a one dimensional lattice, where both species (particles and trap) are mobile and have a drift velocity. We obtain the density as seen from a reference system attached to the…
We study an exactly solvable random walk model with long-range memory on arbitrary networks. The walker performs unbiased random steps to nearest-neighbor nodes and intermittently resets to previously visited nodes in a preferential way,…
We study random walks evolving in continuous time on a one-dimensional lattice where each site $x$ hosts a quenched random potential $U_x$. The potentials on different sites are independent, identically distributed Gaussian random…
We develop a framework for designing density-dependent stochastic resetting protocols to regulate distributions of random walkers on networks. Resetting mechanisms that depend on local densities induce correlations in otherwise…
We consider a specific random graph which serves as a disordered medium for a particle performing biased random walk. Take a two-sided infinite horizontal ladder and pick a random spanning tree with a certain edge weight $c$ for the…