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Coexistence in chase-escape. (arXiv:1807.05594v1 [math.PR])
来源于:arXiv
We study a competitive stochastic growth model called chase-escape where one
species chases another. Red particles spread to adjacent uncolored sites and
blue only to adjacent red sites. Red particles are killed when blue occupies
the same site. If blue has rate-1 passage times and red rate-$\lambda$, a phase
transition occurs for the probability red escapes to infinity on $\mathbb Z^d$,
$d$-ary trees, and the ladder graph $\mathbb Z \times \{0,1\}$. The result on
the tree was known, but we provide a new, simpler calculation of the critical
value, and observe that it is a lower bound for a variety of graphs. We
conclude by showing that red can be stochastically slower than blue, but still
escape with positive probability for large enough $d$ on oriented $\mathbb Z^d$
with passage times that resemble Bernoulli bond percolation. A stronger
conclusion holds in an edge-driven variant of chase-escape on oriented $\mathbb
Z^2$. 查看全文>>