Supremum of the [Airy.sub.2] process minus a parabola on a half line

Let [A.sub.2](t) be the [Airy.sub.2] process. We show that the random variable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] has the same distribution as the one-point marginal of the [Airy.sub.2[right arrow]1] process at time [alpha]. These marginals form a family of distributions crossing ov...

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Bibliographic Details
Published inJournal of statistical physics Vol. 150; no. 3; p. 442
Main Authors Quastel, Jeremy, Remenik, Daniel
Format Journal Article
LanguageEnglish
Published Springer 01.02.2013
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Summary:Let [A.sub.2](t) be the [Airy.sub.2] process. We show that the random variable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] has the same distribution as the one-point marginal of the [Airy.sub.2[right arrow]1] process at time [alpha]. These marginals form a family of distributions crossing over from the GUE Tracy-Widom distribution [F.sub.GUE](x) for the Gaussian Unitary Ensemble of random matrices, to a rescaled version of the GOE Tracy-Widom distribution [F.sub.GOE]([4.sup.1/3]x) for the Gaussian Orthogonal Ensemble. Furthermore, we show that for every [alpha] the distribution has the same right tail decay [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Keywords Airy processes * Last passage percolation * KPZ universality
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-012-0633-4