3 research outputs found
The One-dimensional KPZ Equation and the Airy Process
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.Comment: 15 page