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Coexistence probability in the last passage percolation model is $6 - 8 log 2$

David Coupier; Philippe Heinrich — 2012

Annales de l'I.H.P. Probabilités et statistiques

A competition model on $ℕ^{2}$ 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 $6 - 8 log 2$ . When this happens, we also prove that the central cluster almost surely has a positive density on $ℕ^{2}$ . 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...

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Coexistence probability in the last passage percolation model is 6 - 8 log 2

Coexistence probability in the last passage percolation model is $6 - 8 log 2$