Similarity and Probability Distribution Functions in Many-body Stochastic Processes with Multiplicative Interactions

Akihiro Fujihara, Toshiya Ohtsuki, Hiroshi Yamamoto

Published 2005-08-25Version 1

Analytical and numerical studies on many-body stochastic processes with multiplicative interactions are reviewed. The method of moment relations is used to investigate effects of asymmetry and randomness in interactions. Probability distribution functions of the processes generally have similarity solutions with power-law tails. Growth rates of the system and power-law exponents of the tails are determined via transcendental equations. Good agreement is achieved between analytical calculations and Monte Carlo simulations.