Probability on graphs: A comparison of sampling via random walks and a result for the reconstruction problem
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Date
2010-09
Authors
Ahlquist, Blair, 1979-
Journal Title
Journal ISSN
Volume Title
Publisher
University of Oregon
Abstract
We compare the relaxation times of two random walks - the simple random walk and the metropolis walk - on an arbitrary finite multigraph G. We apply this result to the random graph with n vertices, where each edge is included with probability p = [Special characters omitted.] where λ > 1 is a constant and also to the Newman-Watts small world model. We give a bound for the reconstruction problem for general trees and general 2 × 2 matrices in terms of the branching number of the tree and some function of the matrix. Specifically, if the transition probabilities between the two states in the state space are a and b , we show that we do not have reconstruction if Br( T ) [straight theta] < 1, where [Special characters omitted.] and Br( T ) is the branching number of the tree in question. This bound agrees with a result obtained by Martin for regular trees and is obtained by more elementary methods. We prove an inequality closely related to this problem.
Description
vi, 48 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.
Keywords
Probability, Graphs, Random walks, Reconstruction problem, Metropolis walk, Mixing time