Order of the variance in the discrete Hammersley process with boundaries

A Large deviation principle for last passage times in an asymmetric Bernoulli potential

“…Along the characteristic direction the last passage time at point N (m, n) it is expected to have variance of order O(N 2/3 ) for large N , while in the other directions the fluctuations of G N s , N t to have order of magnitude N 1/2 and they are asymptotically Gaussian. Finally it is possible to prove using similar arguments as in [13] that the order of the variance in the flat edge is o(1).…”

“…Historically, models of last passage percolation for which explicit invariant distributions could be obtained for the embedded particle system [1, 45,47,48], satisifed a Burke-type property that led to invariant boundary corner growth models [3,6,9,10,13,29,33]. The same is true for this model, and we discuss the Burke-type property in Section 2.…”

“…A flat edge for the contact process was observed in [18,19]. The discrete Hammersley model treated in [13,22,23,47] and the inhomogeneous model in [20] allow for an exact derivation of the limiting shape function and they also exhibit two flat edges. Large deviations for the latter were obtained in [21].…”