Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 18 (2013), paper no. 89, 10 pp.
On the average of the Airy process and its time reversal
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.
Electron. Commun. Probab., Volume 18 (2013), paper no. 89, 10 pp.
Accepted: 24 November 2013
First available in Project Euclid: 7 June 2016
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Baik, Jinho; Liu, Zhipeng. On the average of the Airy process and its time reversal. Electron. Commun. Probab. 18 (2013), paper no. 89, 10 pp. doi:10.1214/ECP.v18-2952. https://projecteuclid.org/euclid.ecp/1465315628