临界和部分下临界Galton-Watson随机树在大人口条件下能够收敛到具有唯一无穷分支的Kesten树，即所谓的泛性情形；但是还有部分下临界Galton-Watson树在大人口条件下收敛到具有凝聚现象的极限随机树，即非泛性情形。关于泛性随机树的研究，前人已有了众多结果，而非泛性情形的研究，目前主要是关于单物种的一些结果。本项目致力于研究非泛性多物种Galton-Watson随机树的局部极限性质，主要涉及以下几个方面：（1）非泛性多物种Galton-Watson随机树的分支分布；（2）具有凝聚现象的多物种随机树的实现；（3）带条件的（如大人口时）非泛性多物种Galton-Watson树的局部极限定理。

Conditioned on large population critical and some subcritical Galton-Watson trees converge to Kesten’s tree with an unique infinite spine, which are the so called generic trees. In the non-generic case, subcritical Galton-Watson trees conditioned on large population converge to a limit tree with condensation phenomenon. There are many known results about random trees in generic case, however researches about random trees in non-generic case are mainly on mono-type random trees. This program works on the local limit properties of non-generic multi-type Galton-Watson trees, mainly involving following aspects: The offspring distribution of non-generic multi-type Galton-Watson trees; The realization of multi-type random trees with condensation phenomenon; The local limit theorem of non-generic multi-type Galton-Watson trees conditioned on large population.