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

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

2005-08-25

arxiv.org/abs/cond-mat/0508615v1

Prog. Theor. Phys. Suppl. 162, 212 (2006)

Physics

Condensed Matter

Statistical Mechanics

8 pages, 4 figures, CN-Kyoto proceedings

Scientific paper

10.1143/PTPS.162.212

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.

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