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University of Oregon

1. Montgomery, Aaron. Topics in Random Walks.

Degree: PhD, Department of Mathematics, 2013, University of Oregon

URL: http://hdl.handle.net/1794/13335

We study a family of random walks defined on certain Euclidean lattices that are related to incidence matrices of balanced incomplete block designs. We estimate the return probability of these random walks and use it to determine the asymptotics of the number of balanced incomplete block design matrices. We also consider the problem of collisions of independent simple random walks on graphs. We prove some new results in the collision problem, improve some existing ones, and provide counterexamples to illustrate the complexity of the problem.
*Advisors/Committee Members: Levin, David (advisor).*

Subjects/Keywords: balanced incomplete block designs; collisions of random walks; Markov chains

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APA (6^{th} Edition):

Montgomery, A. (2013). Topics in Random Walks. (Doctoral Dissertation). University of Oregon. Retrieved from http://hdl.handle.net/1794/13335

Chicago Manual of Style (16^{th} Edition):

Montgomery, Aaron. “Topics in Random Walks.” 2013. Doctoral Dissertation, University of Oregon. Accessed August 07, 2020. http://hdl.handle.net/1794/13335.

MLA Handbook (7^{th} Edition):

Montgomery, Aaron. “Topics in Random Walks.” 2013. Web. 07 Aug 2020.

Vancouver:

Montgomery A. Topics in Random Walks. [Internet] [Doctoral dissertation]. University of Oregon; 2013. [cited 2020 Aug 07]. Available from: http://hdl.handle.net/1794/13335.

Council of Science Editors:

Montgomery A. Topics in Random Walks. [Doctoral Dissertation]. University of Oregon; 2013. Available from: http://hdl.handle.net/1794/13335