Solution of urn models by generating functions with applications to social, physical, biological, and network sciences

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Authors
Pickering, William
Issue Date
2016-12
Type
Electronic thesis
Thesis
Language
ENG
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Mathematics
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Abstract
Examples of such an urn model date back to the Ehrenfest "dog-flea" model of molecular diffusion, created in 1907. In this model, one ball is chosen randomly to move to the opposite urn. The model was invented to describe the diffusion of particles within a closed container. This model was later diagonalized by Mark Kac in 1947 by using an innovative generating function method to calculate all eigenvalues and eigenvectors of the Markov transition matrix. We not only improve upon this method, but the models that we solve have a wider range of applications. In addition to the physical application of the Ehrenfest model, we have related such models to social interactions on networks, as well as genetic drift.
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December 2016
School of Science
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Rensselaer Polytechnic Institute, Troy, NY
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