Related papers: First-passage competition with different speeds: p…
Traveling fronts describe the transition between two alternative states in a great number of physical and biological systems. Examples include the spread of beneficial mutations, chemical reactions, and the invasions by foreign species. In…
Consider the model where particles are initially distributed on $\mathbb{Z}^d, \, d\geq 2$, according to a Poisson point process of intensity $\lambda>0$, and are moving in continuous time as independent simple symmetric random walks. We…
We study the random walk of a particle in a compartmentalized environment, as realized in biological samples or solid state compounds. Each compartment is characterized by its length $L$ and the boundaries transmittance $T$. We identify two…
We consider the dynamical evolution of two planets orbiting in the vicinity of a first order mean motion reso- nance while simultaneously undergoing eccentricity damping and convergent migration. Following Goldreich & Schlichting (2014), we…
Most organisms grow in space, whether they are viruses spreading within a host tissue or invasive species colonizing a new continent. Evolution typically selects for higher expansion rates during spatial growth, but it has been suggested…
We investigate a discrete-time two-strain symbiotic epidemic model on complex networks with both random and long-range interactions. Our analysis examines how the co-infection recovery rate ($\mu$), the long-range decay exponent ($\alpha$),…
In this paper we study the diffusion of an SIS-type epidemics on a network under the presence of a random environment, that enters in the definition of the infection rates of the nodes. Accordingly, we model the infection rates in the form…
We use a deterministic model to study two competing viruses spreading over a two-layer network in the Susceptible--Infected--Susceptible (SIS) framework, and address a central problem of identifying the winning virus in a…
We study competing first passage percolation on graphs generated by the configuration model. At time 0, vertex 1 and vertex 2 are infected with the type 1 and the type 2 infection, respectively, and an uninfected vertex then becomes type 1…
We study the evolution of recombination using a microscopic model developed within the frame of the theory of quantitative traits. Two components of fitness are considered: a static one that describes adaptation to environmental factors not…
Competition between species and genotypes is a dominant factor in a variety of ecological and evolutionary processes. Biological dynamics are typically highly stochastic, and therefore, analyzing a competitive system requires accounting for…
We study a two-species competition model in a patchy advective environment, where the species are subject to both directional drift and undirectional random dispersal between patches and there are losses of individuals in the downstream end…
The dynamics leading to extinction or coexistence of competing species is of great interest in ecology and related fields. Recently a model of intra- and interspecific competition between two species was proposed by Gabel et al. [Phys. Rev.…
We consider a symmetric finite-range contact process on $\mathbb{Z}$ with two types of particles (or infections), which propagate according to the same supercritical rate and die (or heal) at rate $1$. Particles of type $1$ can enter any…
We study the time until first occurrence, the first-passage time, of rare density fluctuations in diffusive systems. We approach the problem using a model consisting of many independent random walkers on a lattice. The existence of spatial…
Finding the most powerful node in a dynamic random network, the largest set in a partition-valued stochastic process, or the largest family in an evolving population at a given time, can be a very difficult problem. This is particularly the…
Motivated by modeling the dynamics of a population living in a flowing medium where the environmental factors are random in space, we have studied an asymmetric variant of the one-dimensional contact process, where the quenched random…
We demonstrate that the probability density of a quantum state moving freely in one dimension may decay faster than 1/t. Inverse quadratic and cubic dependences are illustrated with analytically solvable examples. Decays faster than 1/t…
Diseases spread through host populations over the networks of contacts between individuals, and a number of results about this process have been derived in recent years by exploiting connections between epidemic processes and bond…
We propose two models of the evolution of a pair of competing populations. Both are lattice based. The first is a compromise between fully spatial models, which do not appear amenable to analytic results, and interacting particle system…