Random permutations and partitions with structural constraints

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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).