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GOE and Airy_{2\to1} marginal distribution via symplectic Schur functions
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Bisi, Elia and Zygouras, Nikos (2019) GOE and Airy_{2\to1} marginal distribution via symplectic Schur functions. In: Friz, Peter and König, W. and Mukherjee, C. and Olla, S., (eds.) Probability and Analysis in Interacting Physical Systems. VAR75 2016. Springer Proceedings in Mathematics & Statistics, 283 . Cham: Springer. ISBN 9783030153373 (In Press)
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WRAP-GOE-marginal-distribution-sympletic-functions-Zygouras-2019.pdf - Accepted Version - Requires a PDF viewer. Download (851Kb) | Preview |
Official URL: https://doi.org/10.1007/978-3-030-15338-0_7
Abstract
We derive Sasamoto’s Fredholm determinant formula for the Tracy-Widom GOE distribution, as well as the one-point marginal distribution of the Airy2→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 [BZ19a].
| Item Type: | Book Item | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||
| Library of Congress Subject Headings (LCSH): | Schur functions, Marginal distributions | |||||||||
| Series Name: | Springer Proceedings in Mathematics & Statistics | |||||||||
| Publisher: | Springer | |||||||||
| Place of Publication: | Cham | |||||||||
| ISBN: | 9783030153373 | |||||||||
| Book Title: | Probability and Analysis in Interacting Physical Systems. VAR75 2016 | |||||||||
| Editor: | Friz, Peter and König, W. and Mukherjee, C. and Olla, S. | |||||||||
| Official Date: | 25 May 2019 | |||||||||
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| Volume: | 283 | |||||||||
| DOI: | 10.1007/978-3-030-15338-0_7 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | In Press | |||||||||
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