טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentFugenfirov Alexandra
SubjectBranching Particle Systems with Mutually Catalytic
Interactions
DepartmentDepartment of Applied Mathematics
Supervisor Professor Leonid Mytnik


Abstract

We study a continuous time Mutually Catalytic Branching model on the Zd. 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.