Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Drew Sills**, Rutgers University, asills {at} math [dot] rutgers [dot] edu**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Limiting Distributions for Extreme Branch Sizes in Random Recursive Trees

Speaker: **William Goh**, Drexel University

Date: Thursday, March 2, 2006 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

A recursive tree can be viewed as a labeled tree rooted at 1. Let $D$ be the set of nodes of the first generation. A subtree with its root in $D$ is called a branch, which is also a recursive tree if all labels in it are shifted by appropriate constants. The total number of nodes in a branch is called the size of the branch. Let $X_{n}$ and $\widetilde{X}_{n}$ be the random variables marking the minimum branch size and maximum branch size of the tree, respectively. In this talk I will explain how the limiting distribution for $X_{n}$ and $\widetilde{X}_{n}$ are obtained. This is a joint work with Professor Chun Su and Mr. Qunqiang Feng of Department of Statistics and Finance, University of Science and Technology of China.