Random permutations and partitions with structural constraints

该项目将侧重于随机组合结构的渐近研究，例如受各种约束的分区和排列，例如部分的类型或其多样性。这是一个活跃的研究课题，与某些量子系统有着令人兴奋的联系，在这些系统中，由于能量的量子化，分区自然出现。另一个例子是，根据循环结构具有合适分布的随机排列可以模拟具有“选择性”相互作用的粒子系统。研究的兴趣将是典型的行为（如“极限形状”）和极值（如小循环的统计或巨大分量的渐近大小）。

The project will focus on the asymptotic study of random combinatorial structures exemplified by partitions and permutations subject to various constraints, e.g. on the type of parts or their multiplicities. This is an active topic of research, with exciting links to certain quantum systems where partitions appear naturally due to quantization of energy. As another example, random permutations with suitable distributions depending on the cycle structure may model particle systems with "selective" interaction. The interest of research will be both on the typical behaviour (such as the "limit shape") and on extreme values (e.g., statistics of small cycles or the asymptotic size of a giant component).