D. Betea, P.L. Ferrari and A. Occelli The half-space Airy stat process preprint: arXiv:2012.10337 2020 https://arxiv.org/abs/2012.10337
Abstract: We study the multipoint distribution of stationary half-space last passage percolation with exponentially weighted times. We derive both finite-size and asymptotic results for this distribution. In the latter case we observe a new one-parameter process we call half-space Airy stat. It is a one-parameter generalization of the Airy stat process of Baik-Ferrari-Péché, which is recovered far away from the diagonal. All these results extend the one-point results previously proven by the authors.
2019
D. Betea, P.L. Ferrari and A. Occelli Stationary half-space last passage percolation preprint: arXiv:1905.08582 2019 https://arxiv.org/abs/1905.08582
Abstract: In this paper we study stationary last passage percolation (LPP) in half-space geometry. We determine the limiting distribution of the last passage time in a critical window close to the origin. The result is a two-parameter family of distributions: one parameter for the strength of the diagonal bounding the half-space (strength of the source at the origin in the equivalent TASEP language) and the other for the distance of the point of observation from the origin. It should be compared with the one-parameter family giving the BaikâRains distributions for full-space geometry. The result is obtained by using a related integrable model, having Pfaffian structure, together with careful analytic continuation and steepest descent analysis.
P.L. Ferrari and A. Occelli Time-time covariance for last passage percolation with generic initial profile Math. Phys. Anal. Geom., 22: 1 2019 https://doi.org/10.1007/s11040-018-9300-6
Abstract: We consider time correlation for KPZ growth in 1+1 dimensions in a neighborhood of a characteristics. We prove convergence of the covariance with droplet, flat and stationary initial profile. In particular, this provides a rigorous proof of the exact formula of the covariance for the stationary case obtained in [SIGMA 12 (2016), 074]. Furthermore, we prove the universality of the first order correction when the two observation times are close and provide a rigorous bound of the error term. This result holds also for random initial profiles which are not necessarily stationary.
2017
P.L. Ferrari and A. Occelli Universality of the GOE Tracy-Widom distribution for TASEP with arbitrary particle density preprint: arXiv:1704.01291 2017 https://arxiv.org/abs/1704.01291
Abstract: We consider TASEP in continuous time with non-random initial conditions and arbitrary fixed density of particles. We show GOE Tracy-Widom universality of the one-point fluctuations of the associated height function. The result phrased in last passage percolation language is the universality for the point-to-line problem where the line has an arbitrary slope.
0
P.L. Ferrari and A. Occelli Time-time covariance for last passage percolation in half-space preprint:arXiv:2204.06782 0 https://arxiv.org/abs/2204.06782
Abstract: 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.