Log-normal distribution in growing systems with weighted multiplicative interactions

2005/11/25 by Akihiro Fujihara, Satoshi Tanimoto, Fujihara, Akihiro +5
Physics and Astronomy · #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.cond-mat/0511625

4 pages, 4 figures

arxiv created 2006/05/10 · arxiv updated 2009/12/01

Abstract

Many-body stochastic processes with weighted multiplicative interactions are investigated analytically and numerically. An interaction rate between particles with quantities x, y is controlled by a homogeneous symmetric kernel K(x, y) ∝ x^w y^w with a weight parameter w. When w<0, a method of moment inequalities is used to derive log-normal type tails in probability distribution functions. The variance of log-normal distributions is expressed in terms of the weight w and interaction parameters. When interactions are weak and a growth rate of systems is small, in particular, the variance is in proportion to the growth rate. This behavior is totally different from that of one-body stochastic processes, where the variance is independent of the growth rate. At w>0, Monte Carlo simulations show that the processes end up with a winner-take-all state.

Related

• Power-law tails in nonstationary stochastic processes with asymmetrically multiplicative interactions
• On the principle of minimum growth rate in multiplicatively interacting stochastic processes
• Analysis of Discrete Stochastic Population Models with Normal Distribution
• Human Behavior And Lognormal Distribution. A Kinetic Description
• On systems of interacting populations influenced by multiplicative white noise