The calculation of multifractal properties of directed random walks on hierarchic trees with continuous branching

David B Saakian
2012 Journal of Statistical Mechanics: Theory and Experiment  
We consider the hierarchic tree Random Energy Model with continuous branching and calculate the moments of the corresponding partition function. We establish the multifractal properties of those moments. We derive formulas for the normal distribution of random variables, as well as for the general case. We compare our results for the moments of partition function with corresponding results of logarithmic 1-d REM and conjecture a specific power-law tail for the partition function distribution in
more » ... ion distribution in the high-temperature phase. Our results establish a connection between reaction-diffusion equations and multi-scaling.
doi:10.1088/1742-5468/2012/04/p04007 fatcat:v3k34rtrlvgorffgh4gfsviflm