Abstract
We derive Sasamoto’s Fredholm determinant formula for the Tracy-Widom GOE distribution, as well as the one-point marginal distribution of the \(\mathrm{Airy}_{2\rightarrow 1}\) 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].
To Raghu Varadhan with great respect on the occasion of his 75th birthday
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Acknowledgements
This article is dedicated to Raghu Varadhan on the occasion of his 75th birthday. Exact solvability is arguably not within Raghu’s signature style. However, the second author learned about random polymer models and the \(t^{1/3}\) law from Raghu, as being a challenging problem, while he was working under his direction on a somewhat different PhD topic. Since that time he has always had the desire to make some contributions in this direction and would like to thank him for, among other things, having provided this stimulus.
The work of EB was supported by EPSRC via grant EP/M506679/1. The work of NZ was supported by EPSRC via grant EP/L012154/1.
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Bisi, E., Zygouras, N. (2019). GOE and \({\mathrm{Airy}}_{2\rightarrow 1}\) Marginal Distribution via Symplectic Schur Functions. In: Friz, P., König, W., Mukherjee, C., Olla, S. (eds) Probability and Analysis in Interacting Physical Systems. VAR75 2016. Springer Proceedings in Mathematics & Statistics, vol 283. Springer, Cham. https://doi.org/10.1007/978-3-030-15338-0_7
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