M.Sc Student | Shlomov Segev |
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Subject | Interacting Particle Systems with Rapid Stirring |

Department | Department of Industrial Engineering and Management |

Supervisor | Professor Leonid Mytnik |

Full Thesis text |

In this thesis, we study the limiting behavior of an interacting particle system evolving on the lattice. The model is known as the contact process with rapid stirring. It describes the behavior of particles occupying sites on the lattice. We start the process with a single particle at the origin. Each particle may die, jump to a neighbouring site or split. In the case of splitting, one of the offspring takes the place of the parent while the other, the newborn particle, is sent to another site in according to a certain distribution; if the newborn particle lands on an occupied site, its birth is suppressed. Our main goal is to find the sharp asymptotic behavior of the critical branching rate as the jumping rate (also known as the stirring rate) approaches infinity. The critical branching rate is defined as the minimal branching rate such that for each branching rate smaller than the critical branching rate the process extincts with probability one. In addition, we study the asymptotic behavior of the critical branching rate when the location of a newborn particle after branching is distributed over relatively distant sites. We also construct a differential equation for the expected number of particles. The construction methods and the ideas presented can be used to build a differential equation for analogous systems.