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Solution to urn models of pairwise interaction with application to social, physical, and biological sciences.
- Source :
-
Physical Review E . Jul2017, Vol. 96 Issue 1, p1-1. 1p. - Publication Year :
- 2017
-
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]
- Subjects :
- *SOCIAL sciences
*LIFE sciences
*PHYSICAL sciences
Subjects
Details
- Language :
- English
- ISSN :
- 24700045
- Volume :
- 96
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Physical Review E
- Publication Type :
- Academic Journal
- Accession number :
- 124591613
- Full Text :
- https://doi.org/10.1103/PhysRevE.96.012311