The One-dimensional KPZ Equation and the Airy Process

Details The One-dimensional KPZ Equation and the Airy Process The One-dimensional KPZ Equation and the Airy Process

2011-01-24

arxiv.org/abs/1101.4622v2

J. Stat. Mech. (2011) P03020

Physics

Condensed Matter

Statistical Mechanics

15 pages

Scientific paper

10.1088/1742-5468/2011/03/P03020

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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