2022/12/08 by Régine Marchand, Marchand, Régine, Marcovici, Irène +2 · 2 citations
Mathematics · Physics and Astronomy · #60K35 #82B43 #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2212.04399
openalex publication_date 2022/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Corner percolation is a dependent bond percolation model on Z2 introduced by Bálint Tóth, in which each vertex has exactly two incident edges, perpendicular to each other. Gábor Pete has proven in 2008 that under the maximal entropy probability measure, all connected components are finite cycles almost surely. We consider here a regime where West and North directions are preferred with probability p and q respectively, with (p,q) different from (1/2,1/2). We prove that there exists almost surely an infinite number of infinite connected components, which are in fact infinite paths. Furthermore, they all have the same asymptotic slope (2q-1)/(1-2p).