We derive Sasamoto’s Fredholm determinant formula for the Tracy-Widom GOE distribution, as well as the one-point marginal distribution of the 2→1 process, originally derived by Borodin-Ferrari-Sasamoto, as scaling limits of point-to-line and point-to-half-line directed 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 [6].
CITATION STYLE
Bisi, E., & Zygouras, N. (2019). GOE and Airy2→1 Marginal Distribution via Symplectic Schur Functions. In Springer Proceedings in Mathematics and Statistics (Vol. 283, pp. 191–213). Springer. https://doi.org/10.1007/978-3-030-15338-0_7
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