|
Abstract : |
Once upon a time, I began as an analyst. I studied function spaces such as BMO and operators on function spaces, see for example [6,7], but gradually I became more and more interested in probability theory. Some years ago I worked on random coverings and other problems in geometrical probability [8,9], and at present most of my time is devoted to the related field of combinatorial probability, in particular random graphs. This may seem to be very different from the harmonic and functional analysis that I once worked on (and still continue with sometimes), but the difference in methods is not so great. I study random graphs as a probabilist dealing with some combinatorial structures, and my methods are probabilistic and based on analysis, using for example integration theory, functional analysis, martingales and stochastic integration. In this presentation I will give a survey over some recent results on random graphs where I have been at least partly involved. The systematic study of random graphs was started by Erdos and Rnyi [4] in 1960, and the theory has expanded rapidly during the last decade. For a fuller historical account, and for many other results on random graphs, I refer to Bollobs's book [3]. Definitions A random graph is a graph generated by some random procedure. There are many (non-equivalent) ways to define random graphs. The simplest, denoted by G n;m (or one of several common similar notations), where n and m are two integers with 0 m \Gamma, |
