Radial restricted solid-on-solid and etching interface-growth models

An approach to generate radial interfaces is presented. A radial network recursively obtained is used to implement discrete model rules designed originally for the investigation in flat substrates. I used the restricted solid-on-solid and etching models as to test the proposed scheme. The results indicate the Kardar, Parisi, and Zhang conjecture is completely verified leading to a good agreement between the interface radius fluctuation distribution and the Gaussian unitary ensemble. The evolution of the radius agrees well with the generalized conjecture, and the two-point correlation function exhibits also a good agreement with the covariance of the Airy(2) process. The approach can be used to investigate radial interfaces evolution for many other classes of universality.