Date of Award
Doctor of Philosophy (PhD)
coalescing random walk, Feller's branching diffusion, q-voter model, regular random graph, voter model, voter model perturbation
Voter model perturbations can be viewed as voter model (neutral competition) plus asmall perturbation rate. Cox (2017) showed that the biased voter model, viewed as a voter model perturbation, converges to Feller’s branching diffusion under mild mixing condition. We extend this result to a general class of perturbation functions on the setting of r-regular random graphs where the nearest-neighbor voting kernel has a strong mixing property, and prove a low-density diffusive limit of which the convergence of biased voter model is considered as a special case. The other special case considered is the q-voter model whose high-density ODE limit on torus for q close to 1 has been proved by Agarwal, Simper and Durrett (2021). We will introduce the low-density approach we use and show that a mean-field simplification occurs.
Wu, Tianyue, "Rescaled Density Processes of Voter Model Perturbations on r-Regular Random Graphs converge to Feller’s Branching Diffusion" (2023). Dissertations - ALL. 1707.