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arXiv · 1101.4622

The One-dimensional KPZ Equation and the Airy Process

Sylvain Prolhac·Herbert Spohn
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Abstract

Our previous work on the one-dimensional KPZ equation with sharp wedge initial data is extended to the case of the joint height statistics at n spatial points for some common fixed time. Assuming a particular factorization, we compute an n-point generating function and write it in terms of a Fredholm determinant. For long times the generating function converges to a limit, which is established to be equivalent to the standard expression of the n-point distribution of the Airy process.

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Sylvain Prolhac, Herbert Spohn. 2011-03-28. The One-dimensional KPZ Equation and the Airy Process. https://doi.org/10.1088/1742-5468%2F2011%2F03%2Fp03020

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