Atypical Decay Rates for Atypical Heights in Random Recursive Trees

Abstract: We study the large deviation probabilities of the height in random recursive trees. We establish polynomial decay for the upper tail and stretched-exponential decay for the lower tail. Surprisingly, the lower tail involves an atypical pre-factor that grows to infinity slower than any $k$-fold iterated logarithm. Based on a joint work with Xinxin Chen (BNU).