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The Escape Model on a Homogeneous Tree

   
@article{ECP1140,
	author = {George Kordzakhia},
	title = {The Escape Model on a Homogeneous Tree},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {10},
	year = {2005},
	keywords = {},
	abstract = {There are two types of particles  interacting on a homogeneous tree of degree $d+1$. The particles of the first type  colonize  the empty space with exponential rate 1, but cannot take over the vertices that are occupied  by the second type. The  particles of the second type  spread with exponential rate $\lambda$. They colonize   the neighboring vertices that are either vacant or occupied by the  representatives of the opposite type,  and  annihilate  the particles of the type 1 as they reach them. There exists  a critical value $\lambda_c=(2d-1)+\sqrt{(2d-1)^2-1}$ such that the first type survives with positive probability for $\lambda < \lambda_c$, and dies out with probability one for $\lambda > \lambda_c$. We also find the growth profile which characterizes  the rate of growth  of the type 1 in the space-time on the event of survival.},
	pages = {no. 12, 113-124},
	issn = {1083-589X},
	doi = {10.1214/ECP.v10-1140},    
        url = {http://ecp.ejpecp.org/article/view/1140}}