  We derive Sasamoto's Fredholm determinant formula for the Tracy-Widom GOE
distribution, as well as the one-point marginal distribution of the ${\rm
Airy}_{2\to1}$ process, originally derived by Borodin-Ferrari-Sasamoto, as
scaling limits of point-to-line and point-to-half-line last passage percolation
with exponentially distributed waiting times. The asymptotic analysis goes
through new expressions for the last passage times in terms of integrals of
(the continuous analog of) symplectic and classical Schur functions, obtained
recently in [BZ19a].
