Kardar-Parisi-Zhang universality class and the anchored Toom interface.
We revisit the anchored Toom interface and use Kardar-Parisi-Zhang scaling theory to argue that the interface fluctuations are governed by the Airy1 process with the role of space and time interchanged. The predictions, which contain no free parameter, are numerically well confirmed for space-time statistics in the stationary state. In particular, the spatial fluctuations of the interface computed numerically agree well with those given by the GOE edge distribution of Tracy and Widom [Commun. Math. Phys. 177, 727 (1996)].
Institute for Theoretical Physics, Universiteit Utrecht, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands and Instituut-Lorentz, Universiteit Leiden, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands.
G T
GT
Barkema
Institute for Applied Mathematics, Bonn University, Endenicher Allee 60, 53115 Bonn, Germany.
P L
PL
Ferrari
Departments of Mathematics and Physics, Rutgers University, New Brunswick, New Jersey 08854-8019, USA and Institute for Advanced Study, 1 Einstein Drive, Princeton, New Jersey 08540, USA.
J L
JL
Lebowitz
Zentrum Mathematik, TU München, Boltzmannstrasse 3, D-85747 Garching, Germany and Institute for Advanced Study, 1 Einstein Drive, Princeton, New Jersey 08540, USA.
H
H
Spohn