We study the chase-escape percolation model on the 2D square lattice . In this model, prey particles spread to neighboring empty sites at rate p, and predator particles spread only to neighboring sites occupied by prey particles at rate 1, killing the prey particle present at that site. It is found that prey can survive for p>p_c with p_c<1. We estimate the value of p_c to be 0.4943 \pm 0.0005 and the critical exponent for the divergence of the correlation length \nu to be consistent with the 2D isotropic percolation value 4/3. We further show Chase-Escape percolation cannot fully be in the 2D isotropic percolationuniversality class as for p < p_c on a D-dimensional hypercubical lattice, the probability that the number of predators in the absorbing configuration is greater than s is bounded from below by \exp(-Kp^{-1 in contrast to the exponentially decaying cluster size distribution of isotropic percolation . We then study the problem starting from an initial condition with predator particles on all lattice points of the line y=0 and prey particles on the line y=1. In this case, for p_c<p < 1, the center of mass of the  prey and predator fronts travel at the same speed and the two fronts fluctuate, but remain close to each other. We find that the speed of the pinned Chase-Escape front is strictly smaller than the speed of the Eden front when its spreading rate is equal to p and show that it is caused by the prey sites at the leading edge being eaten up by the predator. We study the depinning transition between the two fronts in the model at p= 1. At the depinning point, on a line of length L, the variance of the width of red front increases as L^{\alphaf(t/L^z) where f a scaling function with \alpha\approx 1 and z=1.67}%DIFDELCMD < \pm %%% 0.1 .
Chase-escape percolation is a variation of the standard epidemic spread models . In this model, each site can be in one of three states: unoccupied, occupied by a single prey, or occupied by a single predator. Prey particles spread to neighboring empty sites at rate p, and predator particles spread only to neighboring sites occupied by prey particles at rate 1, killing the prey particle that existed at that site. It was found that the prey can survive with non-zero probability, if p>p_c with p_c<1. Using Monte Carlo simulations on the square lattice, we estimate the value of p_c = 0.49451 \pm 0.00001, and the critical exponents are consistent with the undirected percolation universality class. We define a discrete-time parallel-update version of the model, which brings out the relation between chase-escape and undirected bond percolation. For all p < p_c in D-dimensions, the number of predators in the absorbing configuration has a stretched-exponential distribution in contrast to the exponential distribution in the standard percolation theory. We also study the problem starting from the line initial condition with predator particles on all lattice points of the line y=0 and prey particles on the line y=1. In this case, for p_c<p < 1, the center of mass of the fluctuating prey and predator fronts travel at the same speed . This speed is strictly smaller than the speed of an Eden front with the same value of p, but with no predators. At p= f(t/L^z) where f a scaling function with \alpha\approx 1 and z=1.67}%DIFDELCMD < \pm %%% 1, the fronts undergo a depinning transition. The fluctuations of the front follow Kardar-Parisi-Zhang scaling both above and below this depinning transition .
R
We study the chase-escape percolation model on the 2D square lattice
Chase-escape percolation is a variation of the standard epidemic spread models
R
prey
each site can be in one of three states: unoccupied, occupied by a single prey, or occupied by a single predator. Prey
R
present
that existed
R
is found that
was found that the
R
for
with non-zero probability, if
R
We
Using Monte Carlo simulations on the square lattice, we
R
to be 0.4943
= 0.49451
R
0.0005
0.00001,
R
exponent for the divergence of the correlation length \nu to be
exponents are
R
2D isotropic percolation value 4/3. We further show Chase-Escape percolation cannot fully be in the 2D isotropic percolationuniversality class as for
undirected percolation universality class. We define a discrete-time parallel-update version of the model, which brings out the relation between chase-escape and undirected bond percolation. For all
R
on a D-dimensional hypercubical lattice, the probability that the
in D-dimensions, the
R
is greater than s is bounded from below by \exp(-Kp^{-1
has a stretched-exponential distribution
R
exponentially decaying cluster size distribution of isotropic percolation . We then
exponential distribution in the standard percolation theory. We also
R
an
the line
A
fluctuating
R
and the two fronts fluctuate, but remain close to each other. We find that the speed of the pinned Chase-Escape front
. This speed
R
the Eden front when its spreading rate is equal to p and show that it is caused by the prey sites at the leading edge being eaten up by the predator. We study the depinning transition between the two fronts in the model at
an Eden front with the same value of p, but with no predators. At
D
1. At the depinning point, on a line of length L, the variance of the width of red front increases as L^{\alpha
R
0.1
1, the fronts undergo a depinning transition. The fluctuations of the front follow Kardar-Parisi-Zhang scaling both above and below this depinning transition