Some results on multifractal correlations

We have performed a numerical and analytical study of multifractal correlations in a two-scale random Cantor set. At large distances, for |α - ”’| not very large, we find qualitative agreement between canonical simulation results (also counting results) and the formula recently proposed by Meneveau and Chhabra, following work of Cates and Deutsch. For |α - α’| large, a new correlation scaling function ƒ̃(α, α’, ω) which is linear in log(r) is obtained due to a transition of the moment-scaling function from Cates and Deutsch behavior to a differing behavior for some part of its domain. This linear ƒ̃(α, α’, ω) is consistent with numerical results.