New random geometries and other recent developments in probability

在过去的十年里，出现了一系列新的随机对象，远远超出了经典的随机过程设置。这些物体的共同之处是它们的几何性质：随机树、网络或曲线都将随机性现象与特定的几何结构结合在一起。这一发展的相关性一方面体现在最近授予沃纳的菲尔兹奖，以表彰他在共形不变随机曲线方面的工作，另一方面也体现在从社会学到计算机科学的广泛科学学科对随机网络模型的巨大兴趣。英国的概率学家迫切需要接触到对新兴理论的明确介绍，因为它的发展已经是本世纪初概率论的主要特征之一，而且这些新模型显著增强了应用概率的建模能力。

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.