M.Sc Student | Fugenfirov Alexandra |
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Subject | Branching Particle Systems with Mutually Catalytic Interactions |

Department | Department of Applied Mathematics |

Supervisor | Professor Leonid Mytnik |

We study a continuous time Mutually Catalytic Branching
model on the *Z** ^{d}*. The model describes the
behavior of two different populations of particles, performing random walk on
the lattice in the presence of branching, that is, each particle dies at a
certain rate and is replaced by a random number of offsprings. The branching
rate of a particle in one population is proportional to the number of particles
of another population at the same site. We study the long time behavior for
this model, in particular, coexistence and non-coexistence of two populations
in the long run. Finally, we construct a sequence of renormalized processes and
use duality techniques to investigate its limiting behavior.