Abstract
Circular KPZ interfaces spreading radially in the plane have Gaussian unitary ensemble (GUE) Tracy-Widom (TW) height distribution (HD) and spatial covariance, but what are their statistics if they evolve on the surface of a different background space, such as a bowl, a mountain, or any surface of revolution? To give an answer to this, we report here extensive numerical analyses of several one-dimensional KPZ models on substrates whose size enlarges as , while their mean height increases as usual . We show that the competition between the enlargement and the correlation length () plays a key role in the asymptotic statistics of the interfaces. While systems with have HDs given by GUE and the interface width increasing as , for the HDs are Gaussian, in a correlated regime where . For the special case , a continuous class of distributions exists, which interpolate between Gaussian (for small ) and GUE (for ). Interestingly, the HD seems to agree with the Gaussian symplectic ensemble (GSE) TW distribution for . Despite the GUE HDs for , the spatial covariances present a strong dependence on the parameters and , agreeing with only for , for a given , or when , for a fixed . These results considerably generalize our knowledge on 1D KPZ systems, unveiling the importance of the background space on their statistics.
1 More- Received 19 October 2018
DOI:https://doi.org/10.1103/PhysRevE.99.032140
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