New Random Geometries and Other Recent Developments

The last decade has seen the emergence of a range of new random objects well beyond the classical stochastic process setting. Common to these objects is their geometric nature: Random trees, networksor curves all combine the phenomenon of randomness with a specific geometric structure. The relevanceof this development is demonstrated on the one hand by the recent award of the Fields medal to Wernerfor his work on conformally invariant random curves, on the other hand by the huge amount of interest in random network models coming from a broad range of scientific disciplines from sociology to computerscience. There is a pressing need for probabilists in the UK to be exposed to clear presentations of theemerging theory, since its growth already is one of the dominant features of probability theory at the beginning of this century, and because these new models significantly enhance the modelling capacities inapplied probability.