Year: 2010
Type: article
Abstract: We report on the first exact solution of the Kardar-Parisi-Zhang (KPZ) equation in one dimension, with an initial condition which physically corresponds to the motion of a macroscopically curved height profile. The solution provides a determinantal formula for the probability distribution function of the height h(x,t) for all t>0. In particular, we show that for large t, on the scale t(1/3), the statistics is given by the Tracy-Widom distribution, known already from the Gaussian unitary ensemble of random matrix theory. Our solution confirms that the KPZ equation describes the interface motion in the regime of weak driving force. Within this regime the KPZ equation details how the long time asymptotics is approached.
Source: Physical Review Letters
Authors: Tomohiro Sasamoto, Herbert Spohn
Institutions: Chiba University, Technical University of Munich
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1577096229