This article studies the inhomogeneous geometric polynuclear growth model; the distribution of which is related to Schur functions. We explain a method to derive its distribution functions in both space-like and time-like directions, focusing on the two-time distribution. Asymptotics of the two-time distribution in the KPZ-scaling limit is then considered, extending to two times several single-time distributions in the KPZ universality class.
The first author is partially supported by grant KAW 2015.0270 from the Knut and Alice Wallenberg Foundation and grant 2015-04872 from the Swedish Science Research Council (VR).
We thank a referee for helpful comments, in particular, leading to a better Theorem 4.
"On inhomogeneous polynuclear growth." Ann. Probab. 50 (2) 559 - 590, March 2022. https://doi.org/10.1214/21-AOP1540