2022/04/14 by Patrik L. Ferrari, Ferrari, Patrik L., Alessandra Occelli +1
Computer Science · Mathematics · Physics and Astronomy · #Bayesian Methods and Mixture Models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math-ph #math.MP #math.PR
paper · pdf · doi:10.48550/arxiv.2204.06782
50 pages, 5 figures, LaTeX
arxiv created 2022/04/14 · openalex publication_date 2022/04/14 · arxiv updated 2022/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
This article studies several properties of the half-space last passage percolation, in particular the two-time covariance. We show that, when the two end-points are at small macroscopic distance, then the first order correction to the covariance for the point-to-point model is the same as the one of the stationary model. In order to obtain the result, we first derive comparison inequalities of the last passage increments for different models. This is used to prove tightness of the point-to-point process as well as localization of the geodesics. Unlike for the full-space case, for half-space we have to overcome the difficulty that the point-to-point model in half-space with generic start and end points is not known.