A System of Differential Equations for the Airy Process

Craig A Tracy (University of California, Davis)
Harold Widom (University of California, Santa Cruz)

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.

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Pages: 93-98

Publication Date: June 24, 2003

DOI: 10.1214/ECP.v8-1074

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