1. Solution to urn models of pairwise interaction with application to social, physical, and biological sciences.
- Author
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Pickering, William and Chjan Lim
- Subjects
- *
SOCIAL sciences , *LIFE sciences , *PHYSICAL sciences - Abstract
We investigate a family of urn models that correspond to one-dimensional random walks with quadratic transition probabilities that have highly diverse applications. Well-known instances of these two-urn models are the Ehrenfest model of molecular diffusion, the voter model of social influence, and the Moran model of population genetics. We also provide a generating function method for diagonalizing the corresponding transition matrix that is valid if and only if the underlying mean density satisfies a linear differential equation and express the eigenvector components as terms of ordinary hypergeometric functions. The nature of the models lead to a natural extension to interaction between agents in a general network topology. We analyze the dynamics on uncorrelated heterogeneous degree sequence networks and relate the convergence times to the moments of the degree sequences for various pairwise interaction mechanisms. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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