M.Sc Student | Berezin Roman |
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Subject | Limiting Behaviour of Contact Random Walk |

Department | Department of Industrial Engineering and Management |

Supervisor | Professor Leonid Mytnik |

Full Thesis text |

Interacting particle systems have been a point of great interest to
mathematicians for a long time, in particular the behaviour of those systems,
suitably scaled, as the number of particles in the initial configuration
approaches infinity. In this work we study the limiting behaviour of an
interacting particle system, under the rules of a random walk in a *d*-dimensional
Euclidian space, and a contact process, when the branching speed is on a
smaller scale than the random walk. In our scaling, we start with *N *particles
and let them evolve independently, such that the random walk speed is on the
scale of *N ^{m}*, for some