Revisiting the temporal law in KPZ random growth

Abstract

This article studies the temporal law of the KPZ fixed point. For the stationary geometry, we find the two-time law, which extends the single time law due to Baik-Rains and Ferrari-Spohn. For the droplet geometry, we find a relatively simpler formula for the multi-time law compared to a previous formula of Johansson and the author. These formulas are derived as the scaling limit of corresponding multi-time formulas for geometric last passage percolation.

final version after minor revisions