Research project Concurrent growth on lattice and graphs

Competing growth on an underlying graph structure describes two (or more) entities evolving simultaneously in competition for space. Models of this kind can describe a plethora of phenomena ranging from competing epidemics and concurrent growth of business brands, to the spread of opinions and emergence of social segregation. The central question is if the entities can grow to occupy large parts of the graph simultaneously or if one of them will outcompete the other.

In situations where they can coexist, one can ask about properties of the configuration. This type of models has previously been studied on lattices, where the first models appeared in the mathematical literature some 20 years ago. More recently some of them have also been analyzed on more heterogeneous graph structures. In the present project we will study stochastic models for competing growth, both on lattices and on other structures, aiming at obtaining mathematically rigorous results. We aim to shed new light on the phenomena presented by this class of models by substantial contributions to the theory. The analysis of competition models gives rise to mathematically very interesting and challenging questions, and a rigorous understanding of them constitutes a first step towards being able to analyze more complicated and realistic models.