STATISTICS ON MULTITYPE GALTON-WATSON TREES

In this work is proposed a statistical study of the multitype Galton-Watson trees in order to obtain data on their offspring distribution. The investigation is motivated by some parametric simplified models, based on particular two-type Galton-Watson trees, that we propose for the biological process called angiogenesis, i.e. the growth of new blood vessels. The basic idea of the models is to simplify the structure of a blood vessel as an union of its head and the body of the vessel itself. Moreover, the body of the vessel is conceived as an union of essential units, all with the same size. Then, we apply the structure of certain two-type Galton-Watson trees to the growth of a blood vessel, where the two-type particles are the heads and the essential units of a blood vessel respectively.