Diffusive clustering in the two dimensional voter model
We study the behavior of an interacting particle system known as the voter model in two dimensions. This process provides a simple example of ``critical clustering'' among two colors, say green and black, in the plane. The paper begins with some computer simulations, and a survey of known results concerning the voter model in the three qualitatively distinct cases: three or more dimensions (high), one dimension (low), and two dimensions (critical). Our main theorem, for the planar model, states roughly that at large times t the proportion of green sites on a box of side \(t^{\alpha /2}\) centered at the origin fluctuates with \(\alpha\) according to a time change of the Fisher-Wright diffusion. Some applications of the theorem, and several related results, are described.
scientific article; zbMATH DE number 4076273