Chase-Escape Percolation on the 2D Square Lattice.

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 percolation universality class as for $p

Keywords:

• Lattice (order)
• Mathematical physics
• Percolation
• Lattice (group)
• Initial value problem
• Square lattice
• Physics
• Isotropy
• Correlation function (statistical mechanics)
• Critical exponent

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