68 research outputs found
Queueing with neighbours
In this paper we study asymptotic behaviour of a growth process generated by
a semi-deterministic variant of cooperative sequential adsorption model (CSA).
This model can also be viewed as a particular queueing system with local
interactions. We show that quite limited randomness of the model still
generates a rich collection of possible limiting behaviours
Stability of a growth process generated by monomer filling with nearest-neighbour cooperative effects
We study stability of a growth process generated by sequential adsorption of
particles on a one-dimensional lattice torus, that is, the process formed by
the numbers of adsorbed particles at lattice sites, called heights. Here the
stability of process, loosely speaking, means that its components grow at
approximately the same rate. To assess stability quantitatively, we investigate
the stochastic process formed by differences of heights.
The model can be regarded as a variant of a Polya urn scheme with local
geometric interaction
Probabilistic models motivated by cooperative sequential adsorption
This survey concerns probabilistic models motivated by cooperative sequential
adsorption (CSA) models. CSA models are widely used in physics and chemistry
for modelling adsorption processes in which adsorption rates depend on the
spatial configuration of already adsorbed particles. Corresponding
probabilistic models describe random sequential allocation of particles either
in a subset of Euclidean space, or at vertices of a graph. Depending on a
technical setup these probabilistic models are stated in terms of spatial or
integer-valued interacting birth-and-death processes. In this survey we
consider several such models that have been studied in recent years
On a model of sequential point patterns
A sequential point process motivated by the cooperative sequential adsorption is studied. Analytical properties of the process are considered in details. It is shown that the point process is useful for modelling cluster point patterns. The test on the real life data is carried ou
Gaussian fluctuations of random point measures generated by cooperative sequential adsorption
A finite number of points are sequentially allocated in a finite domain of d-dimensional space. The probability distribution of a point depends on all previously allocated points. We consider a situation when this dependence vanishes as the domain is saturated by points. The law of large numbers and the central limit theorem are proved for the generated sequence of random point measures as the number of points goes to infinit
Long Term Behaviour of Locally Interacting Birth-and-Death Processes
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 both constant vertex degree graphs and star graphs. The model is
motivated by modelling interactions between populations and is related to
interacting particle systems, Gibbs models with unbounded spins, as well as urn
models with interaction.Comment: 26 pages, 2 figure
Spread of infection on homogeneous tree
This paper concerns a probabilistic model of spread of infection on a
homogeneous tree. The model is related to stochastic SIR model on graphs. We
derive an integral equation for the distribution of the waiting time for an
individual to get infected. In a special case the integral equation is
equivalent to the Bernoulli differential equation and implies the classic SIR
model under an appropriate scaling
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