Related papers: Phase transition for a contact process with random…
We study an interacting box-particle system on a one-dimensional periodic ring involving two species of particles $A$ and $B$. In this model, from a randomly chosen site, a particle of species $A$ can hop to its right neighbor with a rate…
A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature…
We study a system of simple random walks on graphs, known as frog model. This model can be described as follows: There are active and sleeping particles living on some graph G. Each active particle performs a simple random walk with…
Population dynamics reflects an underlying birth-death process, where the rates associated with different events may depend on external environmental conditions and on the population density. A whole family of simple and popular…
Using Monte Carlo model of biological evolution we have discovered that populations can switch between two different strategies of their genomes' evolution; Darwinian purifying selection and complementing the haplotypes. The first one is…
In this paper we study long-term evolution of a finite system of locally interacting birth-and-death processes labelled by vertices of a finite connected graph. A detailed description of the asymptotic behaviour is obtained in the case of…
In this paper, we wish to investigate the dynamics of information transfer in evolutionary dynamics. We use information theoretic tools to track how much information an evolving population has obtained and managed to retain about different…
A class of non-local contact processes is introduced and studied using mean-field approximation and numerical simulations. In these processes particles are created at a rate which decays algebraically with the distance from the nearest…
We propose a new perspective on the asymptotic regimes of fast and slow extinction in the contact process on locally converging sequences of sparse finite graphs. We characterise the phase boundary by the existence of a metastable density,…
In many complex systems, states and interaction structure coevolve towards a dynamic equilibrium. For the adaptive contact process, we obtain approximate expressions for the degree distributions that characterize the interaction network in…
Human mobility and activity patterns mediate contagion on many levels, including the spatial spread of infectious diseases, diffusion of rumors, and emergence of consensus. These patterns however are often dominated by specific locations…
We study two famous interacting particle systems, the so-called Richardson's model and the contact process, when we add a stirring dynamics to them. We prove that they both satisfy an asymptotic shape theorem, as their analogues without…
We introduce and study an interacting particle system evolving on the $d$-dimensional torus $(\mathbb Z/N\mathbb Z)^d$. Each vertex of the torus can be either empty or occupied by an individual of type $\lambda \in (0,\infty)$. An…
The contact process is a simple model for the spread of an infection in a structured population. We consider a variant of this process on Bienaym\'e-Galton-Watson trees, where vertices are equipped with a random fitness representing…
The model of directed polymer in a random environment is a fundamental model of interaction between a simple random walk and ambient disorder. This interaction gives rise to complex phenomena and transitions from a central limit theory to…
We study the contact process on a dynamic random~$d$-regular graph with an edge-switching mechanism, as well as an interacting particle system that arises from the local description of this process, called the herds process. Both these…
Consider the following stochastic model for immune response. Each pathogen gives birth to a new pathogen at rate $\lambda$. When a new pathogen is born, it has the same type as its parent with probability $1 - r$. With probability $r$, a…
We consider a model ecosystem of sessile species competing for space. In particular, we consider the system introduced in [Mathiesen et al. Phys. Rev. Lett. 107, 188101 (2011)] where species compete according to a fixed interaction network…
We consider the contact process with infection rate $\lambda$ on a random $(d+1)$-regular graph with $n$ vertices, $G_n$. We study the extinction time $\tau_{G_n}$ (that is, the random amount of time until the infection disappears) as $n$…
The phenomenom of emerging regular spectral features from random interactions is addressed in the context of the interacting boson model. A mean-field analysis links different regions of the parameter space with definite geometric shapes.…