About the Project
The project is devoted to the long term behaviour of a class of Markov processes that can be interpreted as a system of birth-and-death processes, whose components evolve subject to a certain interaction (interacting birth-and-death processes). Originally interacting birth-and-death processes were motivated by modelling competition between populations. In this case they are known as competition processes, which is a class of population probabilistic models. Another interesting case of interacting birth-and-death processes is a growth process motivated by physical phenomenon known as cooperative sequential adsorption (CSA). In CSA diffusing particles can get adsorbed by a material surface, when they hit it. The main peculiarity of CSA is that the adsorbed particles can change the adsorption properties of the material in a sense that they either attract, or repulse other particles. The growth process is
a system of pure birth processes whose components evolve subject to an interaction which is similar to that of CSA. In other words, the components of a growth process can either accelerate, or slow down the growth of each other. In the discrete time setting a growth process can be regarded as an interacting urn model. The latter is a class of random processes with reinforcement closely related to the generalised Polya urn model (another classical probabilistic model).
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