Analytic multivariate generating function for random multiplicative cascade processes

We have found an analytic expression for the multivariate generating function governing all n-point statistics of random multiplicative cascade processes. The variable appropriate for this generating function is the logarithm of the energy density, ln epsilon, rather than epsilon itself. All cumulant statistics become sums over derivatives of ``branching generating functions'' which are Laplace transforms of the splitting functions and completely determine the cascade process. We show that the branching generating function is a generalization of the multifractal mass exponents. Two simple models from fully developed turbulence illustrate the new formalism.Comment: REVTeX, 4 pages, 2 PostScript figs, submitted to PR

Determining source cumulants in femtoscopy with Gram-Charlier and Edgeworth series

Lowest-order cumulants provide important information on the shape of the emission source in femtoscopy. For the simple case of noninteracting identical particles, we show how the fourth-order source cumulant can be determined from measured cumulants in momentum space. The textbook Gram-Charlier series is found to be highly inaccurate, while the related Edgeworth series provides increasingly accurate estimates. Ordering of terms compatible with the Central Limit Theorem appears to play a crucial role even for nongaussian distributions.Comment: 11 pages, 2 figure

Spatial correlations of singularity strengths in multifractal branching processes

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