Chen, Yu-Ting; Choi, Jihyeok; Cox, J. Theodore On the convergence of densities of finite voter models to the Wright-Fisher diffusion. (English. French summary) Zbl 1336.60184 Ann. Inst. Henri Poincaré, Probab. Stat. 52, No. 1, 286-322 (2016). Summary: 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 the density processes. We show by examples that these conditions are satisfied by a large class of voter models on growing finite graphs. Cited in 1 ReviewCited in 8 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60J60 Diffusion processes 60F05 Central limit and other weak theorems 82C22 Interacting particle systems in time-dependent statistical mechanics Keywords:voter models; Wright-Fisher diffusion; interacting particle system; dual processes; semimartingale convergence theorem PDFBibTeX XMLCite \textit{Y.-T. Chen} et al., Ann. Inst. Henri Poincaré, Probab. Stat. 52, No. 1, 286--322 (2016; Zbl 1336.60184) Full Text: DOI arXiv