@article{ECP1422,
author = {Steven Lalley and George Kordzakhia},
title = {An oriented competition model on $Z_+^2$},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {13},
year = {2008},
keywords = {competition, shape theorem, first passage percolation},
abstract = {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 type or Blue type. A vertex flips to the color of a randomly chosen southwest nearest neighbor at exponential rate 2. At time zero there is one Red particle located at $(1,0)$ and one Blue particle located at $(0,1)$. The main result is a partial shape theorem: Denote by $R (t)$ and $B (t)$ the red and blue regions at time $t$. Then (i) eventually the upper half of the unit square contains no points of $B (t)/t$, and the lower half no points of $R (t)/t$; and (ii) with positive probability there are angular sectors rooted at $(1,1)$ that are eventually either red or blue. The second result is contingent on the uniform curvature of the boundary of the corresponding Richardson shape.},
pages = {no. 52, 548-561},
issn = {1083-589X},
doi = {10.1214/ECP.v13-1422},
url = {http://ecp.ejpecp.org/article/view/1422}}