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On the average of the Airy process and its time reversal. (English) Zbl 1305.60101
Summary: 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.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
15B52 Random matrices (algebraic aspects)
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