Atypical Decay Rates for Atypical Heights in Random Recursive Trees

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).