Please use this identifier to cite or link to this item:
http://arks.princeton.edu/ark:/88435/dsp013197xq31q
Title: | On the Scaling Limits of Random Planar Trees and Maps |
Authors: | Lin, Ricky |
Advisors: | Sly, Allan |
Department: | Mathematics |
Certificate Program: | |
Class Year: | 2023 |
Abstract: | In this paper, we discuss connections between discrete and continuous random trees and how we can use that relationship to derive results about the asymptotics of a uniformly distributed random surface. Using Galton-Watson trees as our model for random discrete trees, we show their contour functions converge to a Brownian excursion. We then introduce real trees as a model for continuous trees and show that discrete trees converge in the Gromov-Hausdorff sense to a continuum real tree. Next, we discuss how putting label functions on discrete trees creates a bijection between random labeled trees and random planar maps, which can viewed as a discrete random surface. Finally, we use the scaling limit of random trees and this bijection to describe a uniformly distributed random surface called a Brownian map and present some properties about it |
URI: | http://arks.princeton.edu/ark:/88435/dsp013197xq31q |
Type of Material: | Princeton University Senior Theses |
Language: | en |
Appears in Collections: | Mathematics, 1934-2024 |
Files in This Item:
File | Description | Size | Format | |
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LIN-RICKY-THESIS.pdf | 507.37 kB | Adobe PDF | Request a copy |
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