Supremum of the Airy2 Process Minus a Parabola on a Half LineReport as inadecuate




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Let A2t be the Airy2 process. We show that the random variablesupt≤α A2t −t 2 +min{0,α}2has the same distribution as the one-point marginal of the Airy2→1 process at time α. Thesemarginals form a family of distributions crossing over from the GUE Tracy-Widom distributionFGUEx for the Gaussian Unitary Ensemble of random matrices, to a rescaled versionof the GOE Tracy-Widom distribution FGOE41-3x for the Gaussian Orthogonal Ensemble.Furthermore, we show that for every α the distribution has the same right tail decay e−43x3-2 .Nota general

Artículo de publicación ISI



Author: Quastel, Jeremy; - Remenik Zisis, Daniel; -

Source: http://repositorio.uchile.cl/



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