Stochastic domination in the last passage percolation tree
نویسنده
چکیده
A three colors competition model on (Z) governed by directed last passage percolation is considered. A stochastic domination argument between subtrees of the last passage percolation tree is put forward. Applied to the case of exponential random times, it allows us to prove that coexistence is possible, i.e. three unbounded colored areas occur with positive probability. Furthermore, asymptotic properties of the two competition interfaces are studied. These results are based on the work of Ferrari and Pimentel [3].
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