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We explore probabilistic consequences of correspondences between$q$-Whittaker measures and periodic and free boundary Schur measuresestablished by the authors in the recent paper [arXiv:2106.11922]. The resultis a comprehensive theory of solvability of stochastic models in the KPZ classwhere exact formulas descend from mapping to explicit determinantal andpfaffian point processes. We discover new variants of known results asdeterminantal formulas for the current distribution of the ASEP on the line andnew results such as Fredholm pfaffian formulas for the distribution of thepoint-to-point partition function of the Log Gamma polymer model in half space.In the latter case, scaling limits and asymptotic analysis allow to establishBaik-Rains phase transition for height function of the KPZ equation on the halfline at the origin.

Solvable models in the KPZ class: approach through periodic and free boundary Schur measures