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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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Official URL: https://doi.org/10.1007/978-3-030-15338-0_7

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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
Dates:
DateEvent
25 May 2019Published
Volume: 283
DOI: 10.1007/978-3-030-15338-0_7
Status: Peer Reviewed
Publication Status: In Press
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/L012154/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
EP/M506679/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266

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