Fringe Trees
- 2025-11-10 (Mon.), 10:30 AM
- Auditorium, B1F, Institute of Statistical Science；The tea reception will be held at 10:10.
- Online live streaming through Microsoft Teams will be available.
- Prof. Miklos Bona
- Department of Mathematics, University of Florida, U.S.A.
Abstract
Various parameters of many models of random rooted trees are fairly well understood if they relate to a near-root part of the tree or to global tree structure.
In recent years there has been a growing interest in analysis of the random tree fringe, that is, the tree part close to the leaves. A typical question is the following. Choose a tree variety, like decreasing binary trees, or decreasing plane trees. Then fix n, and choose a random vertex v of a random tree of size n. What can we say about the probability that the distance of v from the closest leaf is equal to a given number k? Then let n go to infinity, and that ck be the limit of these probabilities, if it exists. What can be said about
the sequence of the numbers ck?
Not surprisingly, the level at which we can answer these questions strongly depends on the tree variety we chose. That also means that a wide array of methods can be used in instances of the problem. For example, in some instances a relevant differential equation can be solved in theory, and the difficulty lies in analyzing its solution, while in other cases, it is known that no elementary solution exists. Similarly, in some cases, we can get good estimates for P the numbers ck, while in other cases, it is not even obvious that k ck = 1.
The talk will consist of a sampling of the more interesting results of this exciting area.
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