## Electronic Communications in Probability

### A System of Differential Equations for the Airy Process

#### Abstract

The Airy process is characterized by its $m$-dimensional distribution functions. For $m=1$ it is known that this distribution function is expressible in terms of a solution to Painleve II. We show that each finite-dimensional distribution function is expressible in terms of a solution to a system of differential equations.

#### Article information

Source
Electron. Commun. Probab., Volume 8 (2003), paper no. 10, 93-98.

Dates
Accepted: 24 June 2003
First available in Project Euclid: 18 May 2016

https://projecteuclid.org/euclid.ecp/1463608894

Digital Object Identifier
doi:10.1214/ECP.v8-1074

Mathematical Reviews number (MathSciNet)
MR1987098

Zentralblatt MATH identifier
1067.82031

Rights

#### Citation

Tracy, Craig; Widom, Harold. A System of Differential Equations for the Airy Process. Electron. Commun. Probab. 8 (2003), paper no. 10, 93--98. doi:10.1214/ECP.v8-1074. https://projecteuclid.org/euclid.ecp/1463608894