Chase-Escape percolation on the 2D square lattice

Chase-escape percolation is a variation of the standard epidemic spread models. In this model, each site can be in one three states: unoccupied, occupied by single prey, or predator. Prey particles to neighboring empty sites at rate $p$, and predator only prey $1$, killing particle that existed site. It was found survive with non-zero probability, if $p>p_c$ $p_c<1$. Using Monte Carlo simulations on square lattice, we estimate value $p_c = 0.49451 \pm 0.00001$, critical exponents are consistent undirected universality class. We define discrete-time parallel-update version which brings out relation between chase-escape bond percolation. For all $p < p_c$ $D$-dimensions, number predators absorbing configuration has stretched-exponential distribution contrast exponential theory. also study problem starting from line initial condition lattice points $y=0$ $y=1$. case, for $p_c<p 1$, center mass fluctuating fronts travel same speed. This speed strictly smaller than an Eden front but no predators. At $p=1$, undergo depinning transition. The fluctuations follow Kardar-Parisi-Zhang scaling both above below