Asymptotic function for multigrowth surfaces using power-law noise

Numerical simulations are used to investigate the multiaffine exponent [Formula presented] and multigrowth exponent [Formula presented] of ballistic deposition growth for noise obeying a power-law distribution. The simulated values of [Formula presented] are compared with the asymptotic function [Formula presented] that is approximated from the power-law behavior of the distribution of height differences over time. They are in good agreement for large q. The simulated [Formula presented] is found in the range [Formula presented] This implies that large rare events tend to break the Kardar-Parisi-Zhang universality scaling law at higher order q.