The One-dimensional KPZ Equation and the Airy Process

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.

15 pages

References in corpus (3)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Correlation functions of the one-dimensional attractive Bose gas
• Two-point generating function of the free energy for a directed polymer in a random medium

Cited by in corpus (10)

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• The one-dimensional KPZ equation and its universality class
• The height distribution of the KPZ equation with sharp wedge initial condition: numerical evaluations
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• Maximum of an Airy process plus Brownian motion and memory in KPZ growth
• $N$-point free energy distribution function in one dimensional random directed polymers
• From the totally asymmetric simple exclusion process to the KPZ fixed point
• Analytical Methods and Field Theory for Disordered Systems
• Two-time distribution functions in the Gaussian model of randomly forced Burgers turbulence
• Crossover in the log-gamma polymer from the replica coordinate Bethe Ansatz