Date of Award

5-14-2023

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

Advisor(s)

J. Cox

Keywords

coalescing random walk, Feller's branching diffusion, q-voter model, regular random graph, voter model, voter model perturbation

Abstract

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.

Access

Open Access

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