Speaker : Raoul Normand (Academia Sinica)
Title : Migration under constraints (I): model and discrete computations
Time : 2013-10-21 (Mon) 14:10 -
Place : Seminar Room 722, Institute of Mathematics (NTU Campus)
Abstract: The goal of this two-week talk is to present a model of migration under constraints. This first part focuses on the model itself and on related constructions. The model can be explained as follows. Consider a finite tree, thought of as the genealogical tree of an individual, living on an island. This island provides enough resources to feed, at the same time, some fixed number of individuals. If there are not enough resources to feed everyone, the supernumerary individuals migrate, each to a different island, where they found their own colony. The same process then repeats on all these newly colonized islands. Two interesting quantities can be studied: the total number of people who lived on the initial island, and the number of people who migrated from this island. We shall explain how to encode these quantities through functionals of an exploration process of the tree. Finally, we shall add some randomness to this model, by assuming that this tree is a Galton-Watson tree. In this case, the exploration process is a random walk, and the two quantities described above totally characterize the model. The next talk will show how to compute the limit of these quantities, and the information it provides on the migration process.