Related papers: The Evolution of a Spatial Stochastic Network
We consider a stochastic model for a pathogen population in the presence of an immune response, in which pathogen types are partially ordered by ancestry and the immune system must eliminate ancestor types before it can eliminate their…
This paper analyzes stochastic networks consisting of a set of finite capacity sites where different classes of individuals move according to some routing policy. The associated Markov jump processes are analyzed under a thermodynamic limit…
We consider a class of biologically-motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final…
Representations of population models in terms of countable systems of particles are constructed, in which each particle has a `type', typically recording both spatial position and genetic type, and a level. For finite intensity models, the…
We study a spatial birth-and-death process on the phase space of locally finite configurations $\Gamma^+ \times \Gamma^-$ over $\mathbb{R}^d$. Dynamics is described by an non-equilibrium evolution of states obtained from the Fokker-Planck…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
The effects of stochastic absorption and ejection of molecules by growing droplets have been considered. Both analytical and numerical approaches have been used. They demonstrate the satisfactory coincidence. It is proved that in general…
We consider a basic stochastic particle system consisting of $N$ identical particles with isotropic $k$-particle synchronization, $k\geq 2$. In the limit when both number of particles $N$ and time $t=t(N)$ grow to infinity we study an…
We consider a continuous time Markov process on $\mathbb{N}_0$ which can be interpreted as generalized alternating birth-death process in a non-autonomous random environment. Depending on the status of the environment the process either…
A dynamic model for a random network evolving in continuous time is defined where new vertices are born and existing vertices may die. The fitness of a vertex is defined as the accumulated in-degree of the vertex and a new vertex is…
The growth of a population divided among spatial sites, with migration between the sites, is sometimes modelled by a product of random matrices, with each diagonal elements representing the growth rate in a given time period, and…
We analyze a stochastic particle system of 5 neighbors. Considering eigenvalue problem of transition matrix, we propose a conjecture that asymptotic distribution of the system is determined by the number of specific local patterns in the…
Consider a birth and death chain to model the number of types of a given virus. Each type gives birth to a new type at rate $\lambda$ and dies at rate 1. Each type is also assigned a fitness. When a death occurs either the least fit type…
We study the asymptotic law of a network of interacting neurons when the number of neurons becomes infinite. The dynamics of the neurons is described by a set of stochastic differential equations in discrete time. The neurons interact…
We consider a generic class of stochastic particle-based models whose state at an instant in time is described by a set of continuous degrees of freedom (e.g. positions), and the length of this set changes stochastically in time due to…
In this paper, we investigate the asymptotic behavior of individual-based models describing the evolution of a population structured by a real trait, subject to selection and mutation. We consider two different sets of assumptions: first,…
Population dynamics in random ecological networks are investigated by analyzing a simple deterministic equation. It is found that a sequence of abrupt changes of populations punctuating quiescent states characterize the long time behavior.…
A birth-death-move process with mutations is a Markov model for a system of marked particles in interaction, that move over time, with births and deaths. In addition the mark of each particle may also change, which constitutes a mutation.…
An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We…
The frog model starts with one active particle at the root of a graph and some number of dormant particles at all nonroot vertices. Active particles follow independent random paths, waking all inactive particles they encounter. We prove…