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We report on the asymptotic behaviour of a new model of random walk, we term the bindweed model, evolving in a random environment on an infinite multiplexed tree. The term \textit{multiplexed} means that the model can be viewed as a nearest…
We consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on…
Branching processes are models used to describe populations that reproduce and die over time. In the classical setting, an individual's reproductive capacity remains constant throughout its lifetime. However, in real-world situations,…
Motivated by a host of empirical evidences revealing the bursty character of human dynamics, we develop a model of human activity based on successive switching between an hesitation state and a decision-realization state, with residency…
We derive a self-duality relation for a one-dimensional model of branching and annihilating random walkers with an even number of offsprings. With the duality relation and by deriving exact results in some limiting cases involving fast…
We consider a one dimensional random walk in random environment that is uniformly biased to one direction. In addition to the transition probability, the jump rate of the random walk is assumed to be spatially inhomogeneous and random. We…
During their lifetimes, individuals in populations pass through different states, and the notion of an occupancy time describes the amount of time an individual spends in a given set of states. Questions related to this idea were studied in…
Complex or hostile environments can sometimes inhibit the movement capabilities of diffusive particles or active swimmers, who may thus become stuck in fixed positions. This occurs, for example, in the adhesion of bacteria to surfaces at…
The dynamics of the survival probability of quantum walkers on a one-dimensional lattice with random distribution of absorbing immobile traps are investigated. The survival probability of quantum walkers is compared with that of classical…
We study a system of random walks, known as the frog model, starting from a profile of independent Poisson($\lambda$) particles per site, with one additional active particle planted at some vertex $\mathbf{o}$ of a finite connected simple…
Branching processes are widely used to model the viral epidemic evolution. For more adequate investigation of viral epidemic modelling, we suggest to apply branching processes with transport of particles usually called branching random…
Human interactions and mobility shape epidemic dynamics by facilitating disease outbreaks and their spatial spread across regions. Traditional models often isolate commuting and random mobility as separate behaviors, focusing either on…
Random walks process on networks plays a fundamental role in understanding the importance of nodes and the similarity of them, which has been widely applied in PageRank, information retrieval, and community detection, etc. Individual's…
In this article, we study a branching random walk in an environment which depends on the time. This time-inhomogeneous environment consists of a sequence of macroscopic time intervals, in each of which the law of reproduction remains…
We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. When $d \ge 3$ and the fluctuation of the environment is well moderated by the random walk, we prove a central limit…
In this paper, we deal with a size-variable group of pedestrians moving in a unknown confined environment and searching for an exit. Pedestrian dynamics are simulated by means of a recently introduced microscopic (agent-based) model,…
Computational models of collective behavior in birds has allowed us to infer interaction rules directly from experimental data. Using a generic form of these rules we explore the collective behavior and emergent dynamics of a simulated…
We present an individual-based model for two interacting populations diffusing on lattices in which a strong natural selection develops spontaneously. The models combine traditional local predator-prey dynamics with random walks.…
We study the disorder-induced localisation transition in a three-dimensional network model that belongs to symmetry class C. The model represents quasiparticle dynamics in a gapless spin-singlet superconductor without time-reversal…
A model for the evolution of a finite population in a rugged fitness landscape is introduced and solved. The population is trapped in an evolutionary loop, alternating periods of stasis to periods in which it performs adaptive walks. The…