Spatial correlations of singularity strengths in multifractal branching processes

Abstract

The n-point statistics of singularity strength variables for multiplicative branching processes is calculated from an analytic expression of the corresponding multivariate generating function. The key ingredient is a branching generating function which can be understood as a natural generalisation of the multifractal mass exponents. Various random multiplicative cascade processes pertaining to fully developed turbulence are discussed.Comment: REVTeX, 18 pages, 5 PS figs, submitted to PR