Zhonggen SU

Zhejiang University

Let *n*≥1 be a natural number, *Pn* a set of all integer partitions. To each partition λ assign a probability *P* (λ). Thus we have a finite probability space (*Pn, P*) and are interested in asymptotic behaviors of a typical partition under *P* as *n*→∞. In this talk we particularly focus on random multiplicative measure and Plancherel measure and study the asymptotic fluctuations of the boundary of a Young diagram around its limit shape. It turns out that we need to deal with two cases separately: at the edge and in the bulk. At the edge the fluctuations will asymptotically follow Gumbel and Tracy-Widom extremal laws, while in the bulk asymptotic normality holds.