Coexistence probability in the last passage percolation model is
A competition model on between three clusters and governed by directed last passage percolation is considered. We prove that coexistence, i.e. the three clusters are simultaneously unbounded, occurs with probability . When this happens, we also prove that the central cluster almost surely has a positive density on . Our results rely on three couplings, allowing to link the competition interfaces (which represent the borderlines between the clusters) to some particles in the multi-TASEP, and...