Search

The iterative random subdivision of rectangles is used as a generation model of networks in physics, computer science, and urban planning. However, these researches were independent. We consider some relations in them, and derive fundamental properties for the average lifetime depending on birth-time and the balanced distribution of rectangle faces., identifier:https://dspace.jaist.ac.jp/dspace/handle/10119/13003

The iterative random subdivision of rectangles is used as a generation model of networks in physics, computer science, and urban planning. However, these researches were independent. We consider some relations in them, and derive fundamental properties for the average lifetime depending on birth-time and the balanced distribution of rectangle faces.

It has been known for a few years that the occupation measure of several models of embedded trees converges, after a suitable normalization, to the random measure called ISE (integrated SuperBrownian excursion). Here, we prove a local version of this result: ISE has a (random) Milder continuous density, and the vertical profile of embedded trees converges to this density, at least for some such trees. As a consequence, we derive a formula for the distribution of the density of ISE at a given point. This follows from earlier results by Bousquet-Melou on convergence of the vertical profile at a fixed point. We also provide a recurrence relation defining the moments of the (random) moments of ISE.

We study the difference between the left and right total pathlengths in a random binary tree. The results include exact and asymptotic formulas for moments and an asymptotic distribution that can be expressed in terms of either the Brownian snake or ISE. The proofs are based on computing expectations for a subcritical binary Galton-Watson tree, and studying asymptotics as the Galton-Watson process approaches a critical one., 10th Workshop on the Analysis of AlgorithmsBerkeley, CA, JUL, 2004