The two-time distribution in geometric last-passage percolation

Abstract

We study the two-time distribution in directed last passage percolation with geometric weights in the first quadrant. We compute the scaling limit and show that it is given by a contour integral of a Fredholm determinant.

34 pages. Typos corrected in revised version. In particular sign errors in (2.10) and (2.11) (v2). In the revised version of the paper (v3) the asymptotic analysis has been modified (corrected) and a new section has been added. Minor corrections