Asymptotic function for multigrowth surfaces using power-law noise

Numerical simulations are used to investigate the multiaffine exponent alpha(q) and multigrowth exponent beta(q) of ballistic deposition growth for noise obeying a power-law distribution. The simulated values of beta(q) are compared with the asymptotic function beta(q)=1/q 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 alpha(q) is found in the range 1/qless than or equal toalpha(q)less than or equal to2/(q+1). This implies that large rare events tend to break the Kardar-Parisi-Zhang universality scaling law at higher order q.