Electronic Communications in Probability

A System of Differential Equations for the Airy Process

Craig Tracy and Harold Widom

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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

Permanent link to this document
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

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 05A16: Asymptotic enumeration 33E17: Painlevé-type functions 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)

Keywords
Airy process. Extended Airy kernel. Growth processes. Integrable differential equations

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

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


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