GOE and ${\mathrm{Airy}}_{2\to 1}$ marginal distribution via symplectic Schur functions

Abstract

We derive Sasamoto's Fredholm determinant formula for the Tracy-Widom GOE distribution, as well as the one-point marginal distribution of the ${\mathrm{Airy}}_{2\to 1}$ 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].

19 pages, 2 figures. Typos corrected, references added

References in corpus (6)

• The KPZ equation with flat initial condition and the directed polymer with one free end
• Orthogonal polynomial ensembles in probability theory
• Transition between Airy_1 and Airy_2 processes and TASEP fluctuations
• Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues
• Geometric RSK correspondence, Whittaker functions and symmetrized random polymers
• A determinantal formula for the GOE Tracy-Widom distribution

Cited by in corpus (1)

• The oriented swap process and last passage percolation