  We consider the fluctuations in the stochastic growth of a one-dimensional
interface of height $h(x,t)$ described by the Kardar-Parisi-Zhang (KPZ)
universality class. We study the joint probability distribution function (JPDF)
of the interface heights at two times $t_1$ and $t_2>t_1$, with droplet initial
conditions at $t=0$. In the limit of large times this JPDF is expected to
become a universal function of the time ratio $t_2/t_1$, and of the (properly
scaled) heights $h(x,t_1)$ and $h(x,t_2)$. Using the replica Bethe ansatz
method for the KPZ equation, in [J. Stat. Mech. (2017) 053212] we obtained a
formula for the JPDF in the (partial) tail regime where $h(x,t_1)$ is large and
positive, subsequently found in excellent agreement with experimental and
numerical data [Phys. Rev. Lett. 118, 125701 (2017)]. Here we show that our
results are in perfect agreement with Johansson's recent rigorous expression of
the full JPDF [arXiv:1802.00729 ], thereby confirming the validity of our
methods.
