## Electronic Communications in Probability

### On the average of the Airy process and its time reversal

#### 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.

#### Article information

Source
Electron. Commun. Probab., Volume 18 (2013), paper no. 89, 10 pp.

Dates
Accepted: 24 November 2013
First available in Project Euclid: 7 June 2016

https://projecteuclid.org/euclid.ecp/1465315628

Digital Object Identifier
doi:10.1214/ECP.v18-2952

Mathematical Reviews number (MathSciNet)
MR3145045

Zentralblatt MATH identifier
1305.60101

Rights

#### Citation

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

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