Replica approach to the KPZ equation with half Brownian motion initial condition

Details Replica approach to the KPZ equation with half Brownian motion initial condition Replica approach to the KPZ equation with half Brownian motion initial condition

2011-05-24

arxiv.org/abs/1105.4659v1

Physics

Condensed Matter

Statistical Mechanics

37 pages, 2 figures

Scientific paper

We consider the one-dimensional KPZ equation with half BM initial condition, studied previously through the weakly ASEP. We employ the replica Bethe ansatz and show that the generating function of the exponential moments of the height is expressed as a Fredholm determinant. From this the height distribution and its asymptotics are studied. Furthermore using the replica method we also discuss the multi-point height distribution. We find that some nice properties of the deformed Airy functions play an important role in the analysis.

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