Title: Plancherel type averages for functions of partitions with applications to limit shapes of random partitions
Abstract: Random partitions are of fundamental importance in many subjects, such as representation theory, random permutations and random matrices. A central topic in the study of random partitions is to determine their asymptotic behavior such as limit shapes and fluctuations under Plancherel type measures. In this talk, we will derive polynomiality results on several Plancherel type averages for certain functions of partitions by the difference operator technique, and use them to study the limit shapes of random partitions and random strict partitions.
