%0 Journal Article %1 chen2016convergence %A Chen, Yu-Ting %A Choi, Jihyeok %A Cox, J. Theodore %D 2016 %I Institute of Mathematical Statistics %J Ann. Inst. H. Poincaré Probab. Statist. %K Wright-Fisher_diffusion diffusion_limits duality interacting_particle_systems spatial_coalescent voter_model %N 1 %P 286--322 %R 10.1214/14-aihp639 %T On the convergence of densities of finite voter models to the Wright-Fisher diffusion %U http://dx.doi.org/10.1214/14-AIHP639 %V 52 %X We study voter models defined on large finite sets. Through a perspective emphasizing the martingale property of voter density processes, we prove that in general, their convergence to the Wright–Fisher diffusion only involves certain averages of the voter models over a small number of spatial locations. This enables us to identify suitable mixing conditions on the underlying voting kernels, one of which may just depend on their eigenvalues in some contexts, to obtain the convergence of density processes. We show by examples that these conditions are satisfied by a large class of voter models on growing finite graphs.

@article{chen2016convergence, abstract = {We study voter models defined on large finite sets. Through a perspective emphasizing the martingale property of voter density processes, we prove that in general, their convergence to the Wright–Fisher diffusion only involves certain averages of the voter models over a small number of spatial locations. This enables us to identify suitable mixing conditions on the underlying voting kernels, one of which may just depend on their eigenvalues in some contexts, to obtain the convergence of density processes. We show by examples that these conditions are satisfied by a large class of voter models on growing finite graphs.}, added-at = {2016-03-15T23:15:30.000+0100}, author = {Chen, Yu-Ting and Choi, Jihyeok and Cox, J. Theodore}, biburl = {https://www.bibsonomy.org/bibtex/2a6c406987c394d3906ef197775b3118b/peter.ralph}, doi = {10.1214/14-aihp639}, interhash = {1e6e0f73192868facba5e24d5a8211b2}, intrahash = {a6c406987c394d3906ef197775b3118b}, journal = {Ann. Inst. H. Poincar{\'{e}} Probab. Statist.}, keywords = {Wright-Fisher_diffusion diffusion_limits duality interacting_particle_systems spatial_coalescent voter_model}, month = feb, number = 1, pages = {286--322}, publisher = {Institute of Mathematical Statistics}, timestamp = {2016-03-15T23:15:30.000+0100}, title = {On the convergence of densities of finite voter models to the {Wright}-{Fisher} diffusion}, url = {http://dx.doi.org/10.1214/14-AIHP639}, volume = 52, year = 2016 }