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math.PR2006
Ergodicity and Mixing Properties of the Northeast Model
George Kordzakhia, Steven P. Lalley
The Northeast Model is a spin system on the two-dimensional integer lattice that evolves according to the following rule: Whenever a site's southerly and westerly nearest neighbors…
math.PR2005
A two-species competition model on Z^d
George Kordzakhia, Steven P. Lalley
We consider a two-type stochastic competition model on the integer lattice Z^d. The model describes the space evolution of two ``species'' competing for territory along their bound…
math.PR2005
An Oriented Competition model on Z_{+}^2
George Kordzakhia, Steven Lalley
We consider a two-type oriented competition model on the first quadrant of the two-dimensional integer lattice. Each vertex of the space may contain only one particle of either Red…