Wavelet correlations in hierarchical branching processes

Abstract

A study of correlations in tractable multiparticle cascade models in terms of wavelets reveals many promising features. The selfsimilar construction of the wavelet basis functions and their multiscale localization properties provide a new approach to the statistical analysis and analytical control of hierarchically organized branching processes. The exact analytical solution of several discrete models shows that the wavelet transformation supresses redundancy in the correlation information. Wavelet correlations can be naturally interpreted as correlations between structures (clumps) living on different scales.

Comments: 31 pages, latex, 10 figures (available from authors).