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Topics in Random Walks

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.

Identiferoai:union.ndltd.org:uoregon.edu/oai:scholarsbank.uoregon.edu:1794/13335
Date03 October 2013
CreatorsMontgomery, Aaron
ContributorsLevin, David
PublisherUniversity of Oregon
Source SetsUniversity of Oregon
Languageen_US
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation
RightsAll Rights Reserved.

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