Probabilistic methods for random graphs and random trees

The overall purpose is to continue my successful and internationallyrecognized research on random graphsand random trees using probabilistic methods.

This includes applying existing methods to new problems, but more importantwill be to develop the methods and to introduce new methods to be able tosolve new problems in the area.In connection with this, I plan also to do some work in probability theoryto obtain new general results for Pólya processes and branching processes,both of which have many important applications to random graphs and randomtrees.One important idea that I intend to use is the use of continuous-time stochastic processes to describe thesediscrete problems and their asymptotic behaviour.

I have previously found various versions of this useful on many occasions, and I plan to continue to use and develeop this idea.

This includes, forexample, the use of limit theorems for continuous-time martingales toobtain limits in the form of continuous Gaussian processes such as Brownianmotion and similar processes.The aim is to advance the knowledge of random trees and random graphs by solving a large number of different problems in the area, at the sametime introducing new methods or developing existing ones.There is no single big problem that the project addresses; the aim is towork on a broad front with a variety of different problems and methods,within the scope described here.