%0 Journal Article %1 cox1986diffusive %A Cox, J. Theodore %A Griffeath, David %D 1986 %I Institute of Mathematical Statistics %J The Annals of Probability %K particle_system review voter_model %N 2 %P pp. 347-370 %T Diffusive Clustering in the Two Dimensional Voter Model %U http://www.jstor.org/stable/2243917 %V 14 %X 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 tα/2 centered at the origin fluctuates with α according to a time change of the Fisher-Wright diffusion. Some applications of the theorem, and several related results, are described.

@article{cox1986diffusive, abstract = {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 tα/2 centered at the origin fluctuates with α according to a time change of the Fisher-Wright diffusion. Some applications of the theorem, and several related results, are described.}, added-at = {2012-08-24T21:55:35.000+0200}, author = {Cox, J. Theodore and Griffeath, David}, biburl = {https://www.bibsonomy.org/bibtex/259a39a51efa0a8890b70eee7cfd31170/peter.ralph}, interhash = {014bd9582873826a1573fa4a59c6963a}, intrahash = {59a39a51efa0a8890b70eee7cfd31170}, journal = {The Annals of Probability}, keywords = {particle_system review voter_model}, number = 2, pages = {pp. 347-370}, publisher = {Institute of Mathematical Statistics}, timestamp = {2012-08-24T21:55:35.000+0200}, title = {Diffusive Clustering in the Two Dimensional Voter Model}, url = {http://www.jstor.org/stable/2243917}, volume = 14, year = 1986 }