Browsing Mathematics Theses and Dissertations by Author "Ahlquist, Blair, 1979"
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Ahlquist, Blair, 1979 (University of Oregon, September , 2010)[more][less]Ahlquist, Blair, 1979 20110504T01:19:26Z 20110504T01:19:26Z 201009 http://hdl.handle.net/1794/11144 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. 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 NewmanWatts 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. Committee in charge: David Levin, Chairperson, Mathematics; Christopher Sinclair, Member, Mathematics; Marcin Bownik, Member, Mathematics; Hao Wang, Member, Mathematics; Van Kolpin, Outside Member, Economics en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2010; Probability Graphs Random walks Reconstruction problem Metropolis walk Mixing time Probability on graphs: A comparison of sampling via random walks and a result for the reconstruction problem Thesis
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