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Chase-Escape percolation on the 2D square lattice

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  • Kumar, Aanjaneya
  • Grassberger, Peter
  • Dhar, Deepak

Abstract

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 forever with non-zero probability, if p>pc with pc<1. Earlier simulations showed that pc is very close to 1∕2. Using Monte Carlo simulations in D=2, we estimate the value of pc to be 0.49451±0.00001 and the critical exponents are consistent with the undirected percolation universality class. We check that at pc, the correlation functions at large length scales are rotationally invariant. We define a discrete-time parallel-update version of the model, which brings out the relation between chase-escape and undirected bond percolation. We further show that for all p

Suggested Citation

  • Kumar, Aanjaneya & Grassberger, Peter & Dhar, Deepak, 2021. "Chase-Escape percolation on the 2D square lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 577(C).
    • Handle: RePEc:eee:phsmap:v:577:y:2021:i:c:s0378437121003459
    DOI: 10.1016/j.physa.2021.126072
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