On the average of the Airy process and its time reversal

2013/08/05 by Jinho Baik, Zhipeng Liu, Baik, Jinho +1
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1308.1070

12 pages

arxiv created 2013/11/20 · arxiv updated 2013/11/21

Abstract

We show that the supremum of the average of the Airy process and its time reversal minus a parabola is distributed as the maximum of two independent GUE Tracy-Widom random variables. The proof is obtained by considering a directed last passage percolation model with a rotational symmetry in two different ways. We also review other known identities between the Airy process and the Tracy-Widom distributions.

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