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Chase-Escape percolation on the 2D square lattice

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dc.contributor.author KUMAR, AANJANEYA en_US
dc.contributor.author Grassberger, Peter en_US
dc.contributor.author DHAR, DEEPAK en_US
dc.date.accessioned 2021-06-30T09:19:11Z
dc.date.available 2021-06-30T09:19:11Z
dc.date.issued 2021-09 en_US
dc.identifier.citation Physica A-Statistical Mechanics and Its Applications, 577, 126072. en_US
dc.identifier.issn 0378-4371 en_US
dc.identifier.issn 1873-2119 en_US
dc.identifier.uri http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/5991
dc.identifier.uri https://doi.org/10.1016/j.physa.2021.126072 en_US
dc.description.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 , 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 with . Earlier simulations showed that is very close to . Using Monte Carlo simulations in , we estimate the value of to be and the critical exponents are consistent with the undirected percolation universality class. We check that at , 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 , in dimensions, the probability that the number of predators in the absorbing configuration is greater than is bounded from below by , where is some -independent constant. This is in contrast to the exponentially decaying cluster size distribution in the standard percolation theory. Even so, the scaling function for the cluster size distribution for near decays exponentially: the stretched exponential behavior dominates for , but diverges near . We also study the problem starting from an initial condition with predator particles on all lattice points of the line and prey particles on the line . In this case, for , 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 , but with no predators. This is caused by the prey sites at the leading edge being eaten up by predators. The fluctuations of the front follow KPZ scaling both above and below the depinning transition at . en_US
dc.language.iso en en_US
dc.publisher Elsevier B.V. en_US
dc.subject Phase-Transitions en_US
dc.subject Growth en_US
dc.subject Model en_US
dc.subject 2021-JUN-WEEK5 en_US
dc.subject TOC-JUN-2021 en_US
dc.subject 2021 en_US
dc.title Chase-Escape percolation on the 2D square lattice en_US
dc.type Article en_US
dc.contributor.department Dept. of Physics en_US
dc.identifier.sourcetitle Physica A-Statistical Mechanics and Its Applications en_US
dc.publication.originofpublisher Foreign en_US


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