Year: 2012
Type: dissertation
Abstract: Consider a nearest neighbour random walk Xn on the d-regular tree Td, where d ≥ 3, conditioned on Xn = X0. This is known as the random walk bridge. We derive Gaussianlike tail bounds for the return probabilities of the random walk bridge on the scale of n1/2. This contrasts with the case of the unconditioned random walk, where Gaussian-like tail bounds exists on the scale of n. We introduce the notion of the infinite bridge, which is known to arise as the distributional limit of the random walk bridge. We also establish some preliminary facts about the infinite bridge. By showing that the Brownian Continuum Random Tree (BCRT) is characterized by its random self-similarity property, we prove that the range of the random walk bridge converges in distribution to the BCRT when rescaled by Cn–1/2 for an appropriate constant C.
Source: TSpace (University of Toronto)
Author: Yechen Xu
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2212192431